Arithmetic Progression

Concept: nth term of AP

Fill in the blanks in the following table, given that a is the first term, d the common difference and a_n, the n^th term of the AP.

i. a = 7, d = 3 and n = 8 a_n = ?
ii. a = - 18, n = 10, a_n = 0, d = ?
iii. d = -3, n = 18, a_n = -5, a = ?
iv. a = -18.9, d = 2.5, a_n = 3.6, n = ?
v. a = 3.5, d = 0, n = 105, a_n = ?

Concept: nth term of AP

Choose the correct choice in the following and justify i. 30^th term of the AP: 10, 7, 4, ....., is

1. 28
2. 77
3. -77
4. -87

ii. 11^th term of the AP: -3, -\\frac{1}{2}), 2, ....., is

1. 28
2. 22
3. -38
4. -48\\frac{1}{2})

Concept: Terms of Arithmetic Progression

In the following APs, find the missing terms in the boxes:

i. 2, \\square), 26
ii. _________, 13, _________, 3
iii. 5, _________, _________, 9½
iv. -4, _________, _________, _________, _________, 6
v. _________, 38, _________, _________, _________, -22

Concept: Find 'n' in an AP

Which term of the AP: 3, 8, 13, 18, ......, is 78?

Concept: Number of terms in AP

Find the number of terms in each of the following APs:

i.   7, 13, 19, ......, 205
ii. 18, 15½, 13, ......, -47

Concept: AP nth term formula

Check whether -150 is a term of the AP: 11, 8, 5, 2

Concept: Find a, d, and nth term of AP

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

Concept: Find first term, common difference and nth term

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

Concept: Find n if nth term of an AP is zero

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

Concept: Compute common difference of AP

The 17^th term of an AP exceeds its 10^th term by 7. Find the common difference.

Concept: Find 'n' and 'd' of an AP

Which term of the AP: 3, 15, 27, 39, … will be 132 more than its 54^th term?

Concept: Difference between nth term of 2 APs with same common difference

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

Concept: AP with d = 7. Multiples of 7

How many three-digit numbers are divisible by 7?

Concept: AP with d = 4; multiples of 4

How many multiples of 4 lie between 10 and 250?

Concept: nth term of 2 APs is same

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

Concept: Find AP given some terms of the AP

Determine the AP whose third term is 16 and the 7^th term exceeds the 5^th term by 12.

Concept: Find (n - 19)th term of an AP

Find the 20^th term from the last term of the AP: 3, 8, 13, ...... 253.

Concept: Find first term given sum of some terms of an AP

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

Concept: Word Problem in Arithmetic Progression

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?

Concept: Word Problem in Arithmetic Progression

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