Selina solutions for Mathematics [English] Class 10 ICSE chapter 10 - Arithmetic Progression [Latest edition]

Which of the following sequences are in arithmetic progression?

2, 6, 10, 14, .....

Which of the following sequences are in arithmetic progression?

15, 12, 9, 6, .....

Which of the following sequences are in arithmetic progression?

5, 9, 12, 18, .....

Which of the following sequences are in arithmetic progression?

`1/2, 1/3 , 1/4 , 1/5, ....`

The n^th term of a sequence is (2n – 3), find its fifteenth term.

If the p^th term of an A.P. is (2p + 3); find the A.P.

Find the 24^th term of the sequence:

12, 10, 8, 6, .......

Find the 30^th term of the sequence:

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

Find the 100^th term of the sequence:

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

Find the 50^th term of the sequence:

`1/n, (n + 1)/n, (2n + 1)/n,..........`

Is 402 a term of the sequence:

8, 13, 18, 23, ................. ?  

Find the common difference and 99^th term of the arithmetic progression:

`7 3/4, 9 1/2, 11 1/4, ................` 

How many terms are there in the series 4, 7, 10, 13, ........,148?

How many terms are there in the series 0.5, 0.53, 0.56, ........, 1.1?

How many terms are there in the series `3/4, 1, 1 1/4, ........., 3`?

Which term of the A.P. 1, 4, 7, 10, ....... is 52?

If 5^th and 6^th terms of an A.P. are respectively 6 and 5, find the 11^th term of the A.P.

If t_n represents n^th term of an A.P., t₂ + t₅ – t₃ = 10 and t₂ + t₉ = 17, find its first term and its common difference.

Find the 10^th term from the end of the A.P. 4, 9, 14, .........., 254. 

Determine the arithmetic progression whose 3^rd term is 5 and 7^th term is 9.

Find the 31^st term of an A.P. whose 10^th term is 38 and the 16^th term is 74.

Which term of the series:

21, 18, 15 ....... is –81? 

Can any term of this series be zero? If yes, find the number of terms.

An A.P. consists of 60 terms, If the first and the last terms be 7 and 125 respectively, find the 31^st term.

The sum of the 4^th and the 8^th terms of an A.P. is 24 and the sum of the 6^th and the 10^th terms of the same A.P. is 34. Find the first three terms of the A.P.

If the third term of an A.P. is 5 and the seventh terms is 9, find the 17^th term.

In an A.P., ten times of its tenth term is equal to thirty times of its 30^th term. Find its 40^th term.

How many two-digit numbers are divisible by 3?

Which term of A.P. 5, 15, 25 ………… will be 130 more than its 31st term?

Find the value of p, if x, 2x + p and 3x + 6 are in A.P.

If the 3rd and the 9th terms of an AP are 4 and –8 respectively, which term of this AP is zero?

How many three-digit numbers are divisible by 87?

For what value of n, the n^th terms of the arithmetic progressions 63, 65, 67, ... and 3, 10, 17, ... equal?

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

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

Determine the value of k for which k² + 4k + 8, 2k² + 3k + 6 and 3k² + 4k + 4 are in A.P.

If a, b and c are in A.P. show that 4a, 4b and 4c are in A.P.

If a, b and c are in A.P. show that a + 4, b + 4 and c + 4 are in A.P.

An A.P. consists of 57 terms of which 7^th term is 13 and the last term is 108. Find the 45^th term of this A.P.

4^th term of an A.P. is equal to 3 times its first term and 7^th term exceeds twice the 3^rd term by 1. Find the first term and the common difference.

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

In an A.P., if m^th term is n and n^th term is m, show that its r^th term is (m + n – r).

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

Find the sum of the first 22 terms of the A.P. : 8, 3, –2, ………

How many terms of the A.P. : 24, 21, 18, ................ must be taken so that their sum is 78?

Find the sum of 28 terms of an A.P. whose n^th term is 8n – 5.

Find the sum of all odd natural numbers less than 50.

Find the sum of first 12 natural numbers each of which is a multiple of 7.

Find the sum of first 51 terms of an A.P. whose 2^nd and 3^rd terms are 14 and 18 respectively.

If the sum of first 7 terms of an A.P. is 49 and that of its first 17 terms is 289, find the sum of first n terms of the A.P.

The first term of an A.P. is 5, the last term is 45 and the sum of its terms is 1000. Find the number of terms and the common difference of the A.P.

Find the sum of all natural numbers between 250 and 1000 which are divisible by 9.

The first and the last terms of an A.P. are 34 and 700 respectively. If the common difference is 18, how many terms are there and what is their sum?

In an A.P. the first term is 25, n^th term is –17 and the sum of n terms is 132. Find n and the common difference.

If the 8^th term of an A.P. is 37 and the 15^th term is 15 more than the 12^th term, find the A.P. Also, find the sum of first 20 terms of A.P.

Find the sum of all multiples of 7 lying between 300 and 700.

The sum of n natural numbers is 5n² + 4n. Find its 8^th term.

The fourth term of an A.P. is 11 and the eighth term exceeds twice the fourth term by 5. Find the A.P. and the sum of first 50 terms.

Find three numbers in A.P. whose sum is 24 and whose product is 440.

The sum of three consecutive terms of an A.P. is 21 and the sum of their squares is 165. Find these terms.

The angles of a quadrilateral are in A.P. with common difference 20°. Find its angles. 

Divide 96 into four parts which are in A.P. and the ratio between product of their means to product of their extremes is 15 : 7.

Find five numbers in A.P. whose sum is `12 1/2` and the ratio of the first to the last terms is 2 : 3.

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

The sum of three numbers in A.P. is 15 and the sum of the squares of the extreme terms is 58. Find the numbers. 

Find four numbers in A.P. whose sum is 20 and the sum of whose squares is 120.

Insert one arithmetic mean between 3 and 13.

The angles of a polygon are in A.P. with common difference 5°. If the smallest angle is 120°, find the number of sides of the polygon.

`1/a, 1/b` and `1/c` are in A.P. Show that : bc, ca and ab are also in A.P.

Two cars start together in the same direction from the same place. The first car goes at uniform speed of 10 km h^–1. The second car goes at a speed of 8 km h^–1 in the first hour and thereafter increasing the speed by 0.5 km h^–1 each succeeding hour. After how many hours will the two cars meet?

A sum of Rs. 700 is to be paid to give seven cash prizes to the students of a school for their overall academic performance. If the cost of each prize is Rs. 20 less than its preceding prize; find the value of each of the prizes.

An article can be bought by paying Rs. 28,000 at once or by making 12 monthly installments. If the first installment paid is Rs. 3,000 and every other installment is Rs. 100 less than the previous one, find:

1. amount of installments paid in the 9^th month.
2. total amount paid in the installment scheme.

A manufacturer of TV sets produces 600 units in the third year and 700 units in the 7^th year. Assuming that the production increases uniformly by a fixed number every year, find:

1. the production in the first year.
2. the production in the 10^th year.
3. the total production in 7 years.

Mrs. Gupta repays her total loan of Rs. 1,18,000 by paying installments every month. If the installments for the first month is Rs. 1,000 and it increases by Rs. 100 every month, What amount will she pays as the 30^th installments of loan? What amount of loan she still has to pay after the 30^th installment?

The 6^th term of an A.P. is 16 and the 14^th term is 32. Determine the 36^th term.

If the 3^rd and the 9^th term of an A.P. be 4 and –8 respectively, find which term is zero?

An A.P. consists of 50 terms of which 3^rd term is 12 and the last term is 106. Find the 29^th term of the A.P.

Find the arithmetic mean of –5 and 41.

Find the arithmetic mean of 3x – 2y and 3x + 2y.

Find the arithmetic mean of (m + n)² and (m – n)².

Find the sum of first 10 terms of the A.P.

4 + 6 + 8 + .............

Find the sum of first 20 terms of an A.P. whose first term is 3 and the last term is 57.

How many terms of the series 18 + 15 + 12 + ........ when added together will give 45?

The n^th term of a sequence is 8 – 5n. Show that the sequence is an A.P.

Find the general term (n^th term) and 23^rd term of the sequence 3, 1, –1, –3, ........... . 

Which term of the sequence 3, 8, 13, ........ is 78?

Is –150 a term of 11, 8, 5, 2, .......?

How many two digit numbers are divisible by 3?

How many multiples of 4 lie between 10 and 250?

The sum of the 4^th and the 8^th terms of an A.P. is 24 and the sum of the sixth term and the tenth is 44. Find the first three terms of the A.P.

The sum of first 14 terms of an A.P. is 1050 and its 14^th term is 140. Find the 20^th term.

The 25^th term of an A.P. exceeds its 9^th term by 16. Find its common difference.

For an A.P., show that (m + n)^th term + (m – n)^th term = 2 × m^thterm

If the n^th term of the A.P. 58, 60, 62, .... is equal to the n^th term of the A.P. –2, 5, 12, …., find the value of n.

Which term of the A.P. 105, 101, 97, ........  is the first negative term?

How many three digit numbers are divisible by 7?

Divide 216 into three parts which are in A.P. and the product of two smaller parts is 5040.

Can 2n² – 7 be the n^th term of an A.P.? Explain.

Find the sum of the A.P., 14, 21, 28, ......, 168.

The first term of an A.P. is 20 and the sum of its first seven terms is 2100; find the 31^st term of this A.P.

Find the sum of last 8 terms of the A.P. –12, –10, –8, ……, 58.