Given a= 5, d= 3, An = 50, find n and Sn

In which of the following situations, does the list of numbers involved make as arithmetic progression and why? (i) The taxi fare after each km when the fare is Rs 15 for the first km and Rs 8 for each additional km. (ii) The amount of air present in a cylinder when a vacuum pump removes 1/4 of the air remaining in the cylinder at a time. (iii) The cost of digging a well after every metre of digging, when it costs Rs 150 for the first metre and rises by Rs 50 for each subsequent metre. (iv) The amount of money in the account every year, when Rs 10000 is deposited at compound interest at 8% per annum.

Write first four terms of the A.P. when the first term a and the common difference are given as follows: (i) a = 10, d = 10 (ii) a = -2, d = 0 (iii) a = 4, d = – 3 (iv) a = -1 d = 1/2 (v) a = – 1.25, d = – 0.25

For the following A.P.s, write the first term and the common difference. (i) 3, 1, – 1, – 3 … (ii) -5, – 1, 3, 7 … (iii) 1/3, 5/3, 9/3, 13/3 …. (iv) 0.6, 1.7, 2.8, 3.9 …

Which of the following are APs? If they form an A.P. find the common difference d and write three more terms. (i) 2, 4, 8, 16 … (ii) 2, 5/2, 3, 7/2 …. (iii) -1.2, -3.2, -5.2, -7.2 … (iv) -10, – 6, – 2, 2 … (v) 3, 3 + √2, 3 + 2√2, 3 + 3√2 (vi) 0.2, 0.22, 0.222, 0.2222 …. (vii) 0, – 4, – 8, – 12 … (viii) -1/2, -1/2, -1/2, -1/2 …. (ix) 1, 3, 9, 27 … (x) a, 2a, 3a, 4a … (xi) a, a2, a3, a4 … (xii) √2, √8, √18, √32 … (xiii) √3, √6, √9, √12 … (xiv) 12, 32, 52, 72 … (xv) 12, 52, 72, 73 …

Fill in the blanks in the following table, given that a is the first term, d the common difference and an the nth term of the A.P.

Choose the correct choice in the following and justify: (i) 30th term of the A.P: 10,7, 4, …, is (A) 97 (B) 77 (C) −77 (D) −87

In the following APs find the missing term in the boxes.

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

Find the number of terms in each of the following A.P. (i) 7, 13, 19, …, 205

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

Find the 31st term of an A.P. whose 11th term is 38 and the 16th term is 73.

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

If the 3rd and the 9th terms of an A.P. are 4 and − 8 respectively. Which term of this A.P. is zero.

If 17th term of an A.P. exceeds its 10th term by 7. Find the common difference.

Which term of the A.P. 3, 15, 27, 39,.. will be 132 more than its 54th term?

Two APs have the same common difference. The difference between their 100th term is 100, what is the difference between their 1000th terms?

How many three digit numbers are divisible by 7?

How many multiples of 4 lie between 10 and 250?

For what value of n, are the nth terms of two APs 63, 65, 67, and 3, 10, 17, … equal?

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

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

The sum of 4th and 8th terms of an A.P. is 24 and the sum of the 6th and 10th terms is 44. Find the first three terms of the A.P.

Subba Rao started work in 1995 at an annual salary of Rs 5000 and received an increment of Rs 200 each year. In which year did his income reach Rs 7000?

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

Find the sum of the following APs. (i) 2, 7, 12 ,…., to 10 terms. (ii) − 37, − 33, − 29 ,…, to 12 terms (iii) 0.6, 1.7, 2.8 ,…….., to 100 terms (iv) 1/15, 1/12, 1/10, …… , to 11 terms

Find the sums given below: (ii) 34 + 32 + 30 + ……….. + 10 (iii) − 5 + (− 8) + (− 11) + ………… + (− 230)

In an AP (i) Given a = 5, d = 3, an = 50, find n and Sn. (ii) Given a = 7, a13 = 35, find d and S13. (iii) Given a12 = 37, d = 3, find a and S12. (iv) Given a3 = 15, S10 = 125, find d and a10. (v) Given d = 5, S9 = 75, find a and a9. (vi) Given a = 2, d = 8, Sn = 90, find n and an. (vii) Given a = 8, an = 62, Sn = 210, find n and d. (viii) Given an = 4, d = 2, Sn = − 14, find n and a. (ix) Given a = 3, n = 8, S = 192, find d. (x) Given l = 28, S = 144 and there are total 9 terms. Find a.

How many terms of the AP. 9, 17, 25 … must be taken to give a sum of 636?

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

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

Find the sum of first 22 terms of an AP in which d = 7 and 22nd 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 sum of first 7 terms of an AP is 49 and that of 17 terms is 289, find the sum of first n terms.

Show that a1, a2 … , an , … form an AP where an is defined as below (i) an = 3+4n (ii) an = 9−5n Also find the sum of the first 15 terms in each case.