Q7 of 178 Page 526

How many terms are there in the AP 6, 10, 14, 18, ... , 174?

In the given AP, the first term = a = 6

Common difference = d = 10 - 6 = 4

Last term = 174

To find: No. of terms in the AP.

Since, we know that

a_n = a + (n - 1) × d

∴ 174 = 6 + (n - 1) × 4

⇒ 174 - 6 = 4n - 4

⇒ 168 = 4n - 4

⇒ 168 + 4= 4n

⇒ 4n = 172

⇒ n = 172/4

⇒ n = 43

∴ Number of terms = 43.

Find the nth term of each of the following AP’s:

16, 9, 2, - 5, ...

If the nth term of a progression is (4n - 10) show that it is an AP. Find its

(i) first term,

(ii) common difference, and

(iii) 16th term.

How many terms are there in the AP 41, 38, 35, ..., 8?