NCERT Exemplar solutions for Mathematics [English] Class 10 chapter 5 - Arithematic Progressions [Latest edition]

In an AP, if d = –4, n = 7, a_n = 4, then a is ______.

In an AP, if a = 3.5, d = 0, n = 101, then a_n will be ______.

The list of numbers – 10, – 6, – 2, 2,... is ______.

The 11^th term of the AP: `-5, (-5)/2, 0, 5/2, ...` is ______.

The first four terms of an AP, whose first term is –2 and the common difference is –2, are ______.

The 21^st term of the AP whose first two terms are –3 and 4 is ______.

If the 2^nd term of an AP is 13 and the 5^th term is 25, what is its 7^th term?

Which term of the AP: 21, 42, 63, 84,... is 210?

If the common difference of an AP is 5, then what is a₁₈ – a₁₃?

What is the common difference of an AP in which a₁₈ – a₁₄ = 32?

Two APs have the same common difference. The first term of one of these is –1 and that of the other is – 8. Then the difference between their 4^th terms is ______.

If 7 times the 7^th term of an AP is equal to 11 times its 11^th term, then its 18^th term will be ______.

The 4^th term from the end of the AP: –11, –8, –5, ..., 49 is ______.

The famous mathematician associated with finding the sum of the first 100 natural numbers is ______.

If the first term of an AP is –5 and the common difference is 2, then the sum of the first 6 terms is ______.

The sum of first 16 terms of the AP: 10, 6, 2,... is ______.

In an AP if a = 1, a_n = 20 and S_n = 399, then n is ______.

The Sum of first five multiples of 3 is ______.

Which of the following form an AP? Justify your answer.

–1, –1, –1, –1,...

Which of the following form an AP? Justify your answer.
0, 2, 0, 2,...

Which of the following form an AP? Justify your answer.
1, 1, 2, 2, 3, 3,...

Which of the following form an AP? Justify your answer.

11, 22, 33,...

Which of the following form an AP? Justify your answer.

`1/2, 1/3, 1/4, ...`

Which of the following form an AP? Justify your answer.

2, 2², 2³, 2⁴,...

Which of the following form an AP? Justify your answer.

`sqrt(3), sqrt(12), sqrt(27), sqrt(48)`

Justify whether it is true to say that `-1, - 3/2, -2, 5/2,...` forms an AP as a₂ – a₁ = a₃ – a₂.

For the AP: –3, –7, –11, ..., can we find directly a₃₀ – a₂₀ without actually finding a₃₀ and a₂₀? Give reasons for your answer.

Two APs have the same common difference. The first term of one AP is 2 and that of the other is 7. The difference between their 10^th terms is the same as the difference between their 21^st terms, which is the same as the difference between any two corresponding terms. Why?

Is 0 a term of the AP: 31, 28, 25, ...? Justify your answer.

The taxi fare after each km, when the fare is Rs 15 for the first km and Rs 8 for each additional km, does not form an AP as the total fare (in Rs) after each km is 15, 8, 8, 8,... Is the statement true? Give reasons.

In which of the following situations, do the lists of numbers involved form an AP? Give reasons for your answers.

The fee charged from a student every month by a school for the whole session, when the monthly fee is Rs 400.

In which of the following situations, do the lists of numbers involved form an AP? Give reasons for your answers.

The fee charged every month by a school from Classes I to XII, when the monthly fee for Class I is Rs 250, and it increases by Rs 50 for the next higher class.

In which of the following situations, do the lists of numbers involved form an AP? Give reasons for your answers

The amount of money in the account of Varun at the end of every year when Rs 1000 is deposited at simple interest of 10% per annum.

In which of the following situations, do the lists of numbers involved form an AP? Give reasons for your answers.

The number of bacteria in a certain food item after each second, when they double in every second.

Justify whether it is true to say that the following are the n^th terms of an AP.

2n – 3

Justify whether it is true to say that the following are the n^th terms of an AP.

3n² + 5

Justify whether it is true to say that the following are the n^th terms of an AP.

1 + n + n²

Match the APs given in column A with suitable common differences given in column B.

Verify that the following is an AP, and then write its next three terms.

`0, 1/4, 1/2, 3/4, ...`

Verify that the following is an AP, and then write its next three terms.

`5, 14/3, 13/3, 4,...`

Verify that the following is an AP, and then write its next three terms.

`sqrt(3), 2sqrt(3), 3sqrt(3),...`

Verify that the following is an AP, and then write its next three terms.

a + b, (a + 1) + b, (a + 1) + (b + 1),...

Verify that the following is an AP, and then write its next three terms.

a, 2a + 1, 3a + 2, 4a + 3,...

Write the first three terms of the APs when a and d are as given below:

a = `1/2`, d = `-1/6`

Write the first three terms of the APs when a and d are as given below:

a = –5, d = –3

Write the first three terms of the APs when a and d are as given below:

a = `sqrt(2)`, d = `1/sqrt(2)`

Find a, b and c such that the following numbers are in AP: a, 7, b, 23, c.

Determine the AP whose fifth term is 19 and the difference of the eighth term from the thirteenth term is 20.

The 26^th, 11^th and the last term of an AP are 0, 3 and `- 1/5`, respectively. Find the common difference and the number of terms.

The sum of the 5^th and the 7^th terms of an AP is 52 and the 10^th term is 46. Find the AP.

Find the 20^th term of the AP whose 7^th term is 24 less than the 11^th term, first term being 12.

If the 9^th term of an AP is zero, prove that its 29^th term is twice its 19^th term.

Find whether 55 is a term of the A.P. 7, 10, 13,... or not. If yes, find which term is it.

Determine k so that k² + 4k + 8, 2k² + 3k + 6, 3k² + 4k + 4 are three consecutive terms of an AP.

Split 207 into three parts such that these are in AP and the product of the two smaller parts is 4623.

The angles of a triangle are in AP. The greatest angle is twice the least. Find all the angles of the triangle.

If the n^th terms of the two APs: 9, 7, 5,... and 24, 21, 18,... are the same, find the value of n. Also find that term.

If sum of 3^rd and 8^th terms of an A.P. is 7 and sum of 7^th and 14^th terms is –3 then find the 10^th term.

Find the 12^th term from the end of the AP: –2, –4, –6,..., –100.

Which term of the AP: 53, 48, 43,... is the first negative term?

How many numbers lie between 10 and 300, which when divided by 4 leave a remainder 3?

Find the sum of two middle most terms of the AP `-4/3, -1 (-2)/3,..., 4 1/3.`

The first term of an AP is –5 and the last term is 45. If the sum of the terms of the AP is 120, then find the number of terms and the common difference.

Find the sum:

1 + (–2) + (–5) + (–8) + ... + (–236)

Find the sum:

`4 - 1/n + 4 - 2/n + 4 - 3/n + ...` upto n terms

Find the sum:

`(a - b)/(a + b) + (3a - 2b)/(a + b) + (5a - 3b)/(a + b) +` ... to 11 terms

Which term of the AP: –2, –7, –12,... will be –77? Find the sum of this AP upto the term –77.

If a_n = 3 – 4n, show that a₁, a₂, a₃,... form an AP. Also find S₂₀.

In an AP, if S_n = n(4n + 1), find the AP.

In an A.P., if S_n = 3n² + 5n and a_k = 164, find the value of k.

If S_n denotes the sum of first n terms of an AP, prove that S₁₂ = 3(S₈ – S₄)

Find the sum of first 17 terms of an AP whose 4^th and 9^th terms are –15 and –30 respectively.

If sum of first 6 terms of an AP is 36 and that of the first 16 terms is 256, find the sum of first 10 terms.

Find the sum of all the 11 terms of an AP whose middle most term is 30.

Find the sum of last ten terms of the AP: 8, 10, 12,.., 126.

Find the sum of first seven numbers which are multiples of 2 as well as of 9.

How many terms of the AP: –15, –13, –11,... are needed to make the sum –55? Explain the reason for double answer.

The sum of first n terms of an A.P. whose first term is 8 and the common difference is 20 equal to the sum of first 2n terms of another A.P. whose first term is – 30 and the common difference is 8. Find n.

Kanika was given her pocket money on Jan 1^st, 2008. She puts Rs 1 on Day 1, Rs 2 on Day 2, Rs 3 on Day 3, and continued doing so till the end of the month, from this money into her piggy bank. She also spent Rs 204 of her pocket money, and found that at the end of the month she still had Rs 100 with her. How much was her pocket money for the month?

Yasmeen saves Rs 32 during the first month, Rs 36 in the second month and Rs 40 in the third month. If she continues to save in this manner, in how many months will she save Rs 2000?

The sum of the first five terms of an AP and the sum of the first seven terms of the same AP is 167. If the sum of the first ten terms of this AP is 235, find the sum of its first twenty terms.

Find the sum of those integers between 1 and 500 which are multiples of 2 as well as of 5.

Find the sum of those integers from 1 to 500 which are multiples of 2 as well as of 5.

Find the sum of those integers from 1 to 500 which are multiples of 2 or 5.

[Hint (iii) : These numbers will be : multiples of 2 + multiples of 5 – multiples of 2 as well as of 5]

The eighth term of an AP is half its second term and the eleventh term exceeds one third of its fourth term by 1. Find the 15^th term.

An AP consists of 37 terms. The sum of the three middle most terms is 225 and the sum of the last three is 429. Find the AP.

Find the sum of the integers between 100 and 200 that are

1. divisible by 9
2. not divisible by 9

[Hint (ii) : These numbers will be : Total numbers – Total numbers divisible by 9]

The ratio of the 11^th term to the 18^th term of an AP is 2 : 3. Find the ratio of the 5^th term to the 21^st term, and also the ratio of the sum of the first five terms to the sum of the first 21 terms.

Show that the sum of an AP whose first term is a, the second term b and the last term c, is equal to `((a + c)(b + c - 2a))/(2(b - a))`

Solve the equation

– 4 + (–1) + 2 + ... + x = 437

Jaspal Singh repays his total loan of Rs. 118000 by paying every month starting with the first instalment of Rs. 1000. If he increases the instalment by Rs. 100 every month, what amount will be paid by him in the 30^th instalment? What amount of loan does he still have to pay after the 30^th instalment?

The students of a school decided to beautify the school on the Annual Day by fixing colourful flags on the straight passage of the school. They have 27 flags to be fixed at intervals of every 2 m. The flags are stored at the position of the middle most flag. Ruchi was given the responsibility of placing the flags. Ruchi kept her books where the flags were stored. She could carry only one flag at a time. How much distance did she cover in completing this job and returning back to collect her books? What is the maximum distance she travelled carrying a flag?