Exercise 5.2 (Arithmetic Progression)

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:

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 Choose the correct choice in the following and justify :

(i) 30^th term of the AP: 10, 7, 4, . . . , is
(A) 97
(B) 77
(C) -77
(D) -87

(ii) 11^th term of the AP: – 3, -1/2, 2, ..., is
(A) 28
(B) 22
(C) -38
(D) -48.5

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

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

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

(i) 7, 13, 19, . . . , 205

(ii) 18, $15\frac{1}{2}$, 13, . . . , – 47

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

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

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

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

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

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

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?

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 n^th terms of two APs: 63, 65, 67, . . . and 3, 10, 17, . . . equal?

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

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

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.

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 savings by Rs. 1.75. If in the n^th week, her weekly savings become Rs. 20.75, find n.