# The sum of first four terms of an A.P is 56. The sum of the last four terms is 112. If its first term is 11, then find the number of terms

**Solution:**

Let the A.P be a, (a + d), (a + 2d), (a + 3d), .... a + (n - 2) d, a + (n - 1)d

It is given that

Sum of the first four terms = 56

⇒ a + (a + d) + (a + 2d) + (a + 3d) = 56

⇒ 4a + 6d = 56

⇒ 4 x 11 + 6d = 56

⇒ 6d = 56 - 44

⇒ d = 12/6

⇒ d = 2

Sum of last four terms

⇒ [a + (n - 4) d] +[a + (n - 3) d] + [a + (n - 2) d] + [a + (n - 1) d] = 112

⇒ 4a + (4n - 10) d = 112

⇒ 4 x 11 + (4n - 10) x 2 = 112

⇒ 44 + 8n - 20 = 112

⇒ 8n = 112 - 24

⇒ n = 88/8

⇒ n = 11

Thus, the number of terms of the A.P is 11

NCERT Solutions Class 11 Maths Chapter 9 Exercise ME Question 12

## The sum of first four terms of an A.P is 56. The sum of the last four terms is 112. If its first term is 11, then find the number of terms

**Summary:**

Therefore, knowing the sum of the first four terms of the A.P is 56 and the sum of the last four terms is 112 we found out the number of terms in the A.P is 11