ML Aggarwal solutions for Understanding ICSE Mathematics [English] Class 10 chapter 9 - Arithmetic and Geometric Progressions [Latest edition]

For the following APs, write the first term and the common difference:

3, 1, –1, –3, ...

For the following A.P.s, write the first term a and the common difference d: `(1)/(3), (5)/(3),(9)/(3),(13)/(3)`,...

For the following A.P.s, write the first term a and the common difference d: – 3.2, – 3, – 2.8, – 2.6, …

Write first four terms of the A.P. when the first term a and the common differenced are given as follows:

 a = 10, d = 10

Write first four terms of the A.P. when the first term a and the common differenced are given as follows:

a = -2, d = 0

Write first four terms of the A.P. when the first term a and the common differenced are given as follows:

a = 4, d = -3

Write first four terms of the A.P., when the first term a and the common difference d are given as follows : `"a" = (1)/(2), "d" = -(1)/(6)`

Which of the following lists of numbers form an A.P.? If they form an A.P., find the common difference d and write the next three terms : 4, 10, 16, 22,…

Which of the following lists of numbers form an A.P.? If they form an A.P., find the common difference d and write the next three terms : – 2, 2, – 2, 2,…..

Which of the following lists of numbers form an A.P.? If they form an A.P., find the common difference d and write the next three terms : 2, 4, 8, 16,….

Which of the following lists of numbers form an A.P.? If they form an A.P., find the common difference d and write the next three terms : `2, (5)/(2), 3, (7)/(2)`,...

Which of the following lists of numbers form an A.P.? If they form an A.P., find the common difference d and write the next three terms :  – 10, – 6, – 2, 2,….

Which of the following lists of numbers form an A.P.? If they form an A.P., find the common difference d and write the next three terms : 1², 3², 5², 7²,...

Which of the following lists of numbers form an A.P.? If they form an A.P., find the common difference d and write the next three terms : 1, 3, 9, 27,...

Which of the following lists of numbers form an A.P.? If they form an A.P., find the common difference d and write the next three terms : `sqrt(2), sqrt(8), sqrt(18), sqrt(32)`,...

Which of the following lists of numbers form an A.P.? If they form an A.P., find the common difference d and write the next three terms : `3, 3 + sqrt(2), 3 + 2sqrt(2), 3 + 3sqrt(2)`,...

Which of the following lists of numbers form an A.P.? If they form an A.P., find the common difference d and write the next three terms : `sqrt(3), sqrt(6), sqrt(9), sqrt(12)`,...

Which of the following lists of numbers form an A.P.? If they form an A.P., find the common difference d and write the next three terms : a, 2a, 3a, 4a,...

Which of the following lists of numbers form an A.P.? If they form an A.P., find the common difference d and write the next three terms : a, 2a + 1, 3a + 2, 4a + 3,...

Find the A.P. whose nth term is 7 – 3K. Also find the 20th term.

Find the indicated terms in each of following A.P.s: 1, 6, 11, 16, …; a₂₀

Find the indicated terms in each of following A.P.s: – 4, – 7, – 10, – 13, …, a₂₅, a_n

Find the nth term and the 12th term of the list of numbers: 5, 2, – 1, – 4, …

Find the 8th term of the A.P. whose first term is 7 and common difference is 3.

 If the common difference of an A.P. is – 3 and the 18th term is – 5, then find its first term.

If the first term of an A.P. is – 18 and its 10th term is zero, then find its common difference.

Which term of the A.P. 3, 8, 13, 18, … is 78?

Which term of the A.P. 7, 13, 19, … is 205?

Which term of the A.P. `18, 15(1)/(2)`, 13, ... is – 47?

Check whether -150 is a term of the A.P. 11, 8, 5, 2, ....

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

Is 0 a term of the A.P. 31,28, 25,…? Justify your answer.

Find the 20^th term from the last term of the A.P. 3, 8, 13, …, 253.

Find the 12th from the end of the A.P. – 2, – 4, – 6, …; – 100.

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

Which term of the A.P. 53, 48, 43,… is the first negative term?

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

Determine the A.P. whose 3^rd term is 16 and the 7^th term exceeds the 5^th term by 12.

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

Find the 31^st term of an A.P. whose 11^th term is 38 and 6^th term is 73.

If the seventh term of an A.P. is `(1)/(9)` and its ninth term is `(1)/(7)`, find its 63rd term.

The 15th term of an A.P. is 3 more than twice its 7th term. If the 10th term of the A.P. is 41, find its nth term.

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

The sum of 2nd and 7th terms of an A.P. is 30. If its 15th term is 1 less than twice its 8th term, find the A.P.

If 8th term of an A.P. is zero, prove that its 38th term is triple of its 18th term.

Which term of the A.P. 3, 10, 17, .......... will be 84 more than its 13^th term?

If the nth terms of the two A.g.s 9, 7, 5, … and 24, 21, 18, … are the same, find the value of n. Also, find that term

How many two digit numbers are divisible by 3?

Find the number of natural numbers between 101 and 999 which are divisible by both 2 and 5.

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

If the numbers n – 2, 4n – 1 and 5n + 2 are in A.P., find the value of n.

The sum of three numbers in A.P. is 3 and their product is – 35. Find the numbers.

The sum of three numbers in A.P. is 30 and the ratio of first number to the third number is 3 : 7. Find the numbers.

The sum of the first three terms of an A.P.is 33. If the product of the first and the third terms exceeds the second term by 29, find the A.P.

A man starts repaying a loan as first instalment of Rs 500. If he increases the instalment by Rs 25 every month, what,amount will he pay in the 30th instalment?

Ramkali saved Rs 5 in the first week of a year and then increased her weekly saving by Rs 1.75. If in the n^th week, her week, her weekly savings become Rs 20.75, find n.

Justify whether it is true to say that the following are the nth terms of an A.P. 2n – 3

Justify whether it is true to say that the following are the nth terms of an A.P. n² + 1

Find the sum of the following APs:

2, 7, 12, ..., to 10 terms.

Find the sum of the following APs.

`1/15, 1/12, 1/10`, ......, to 11 terms.

Find the sum given below:

34 + 32 + 30 + ... + 10

How many terms of the A.P. 27, 24, 21, …, should be taken so that their sum is zero?

Find the sum given below:

–5 + (–8) + (–11) + ... + (–230)

In an AP: Given a = 5, d = 3, a_n = 50, find n and S_n.

In an AP, given a = 7, a₁₃ = 35, find d and S₁₃.

In an A.P. (with usual notations) : given d = 5, S₉ = 75, find a and a₉ 

In an A.P. (with usual notations) : given a = 8, a_n = 62, S_n = 210, find n and d

 In an AP given a = 3, n = 8, S_n = 192, find d.

The first term of an A.P. is 5, the last term is 45 and the sum is 400. Find the number of terms and the common difference.

The sum of first 15 terms of an A.P. is 750 and its first term is 15. Find its 20^th term.

The first and last terms of an AP are 17 and 350, respectively. If the common difference is 9, how many terms are there, and what is their sum?

Solve for x : 1 + 4 + 7 + 10 + … + x = 287.

How many terms of the A.P. 25, 22, 19, … are needed to give the sum 116 ? Also find the last term.

How many terms of the A.P. 24, 21, 18, … must be taken so that the sum is 78? Explain the double answer.

Find the sum of first 22 terms of an AP in which d = 7 and 22^nd term is 149.

Find the sum of first 51 terms of an AP whose second and third terms are 14 and 18 respectively.

If the third term of an A.P. is 1 and 6th term is – 11, find the sum of its first 32 terms.

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.

Show that a₁, a₂, a₃, … form an A.P. where a_n is defined as a_n = 3 + 4n. Also find the sum of first 15 terms.

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

 Find the common difference of an A.P. whose first term is 5 and the sum of first four terms is half the sum of next four terms.

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.

The sum of first six terms of an arithmetic progression is 42. The ratio of the 10th term to the 30th term is `(1)/(3)`. Calculate the first and the thirteenth term.

In an A.P., the sum of its first n terms is 6n – n². Find is 25th term.