In an AP, the first term is -4, the last term is 29 and the sum of all

1.	In an AP, the first term is -4, the last term is 29 and the sum of all its terms is 150. Find its common difference.
Answer» Let d be the common difference. Given: first term = a = -4 last term = l = 29 Sum of all the terms = S_n = 150 S_n = n/2[a + l] 150 = n/2[-4 + 29] n = 12 There are 12 terms in total. Therefore, 29 is the 12th term of the AP. Now, 29 = -4 + (12 – 1)d 29 = -4 + 11d d = 3 The common difference is 3.

In an AP, the first term is -4, the last term is 29 and the sum of all its terms is 150. Find its common difference.

Answer»

Let d be the common difference.

Given:

first term = a = -4

last term = l = 29

Sum of all the terms = S_n = 150

S_n = n/2[a + l]

150 = n/2[-4 + 29]

n = 12

There are 12 terms in total.

Therefore, 29 is the 12th term of the AP.

Now, 29 = -4 + (12 – 1)d

29 = -4 + 11d

d = 3

The common difference is 3.