Question

If The 6th term of an a.p 37 and the sum of the first term is 147, find the ,first term And fifteen term

Answer 1

Correct Question:-

If the 6th term of an AP is 37 and the sum of first 6 terms is 147 , find the first term and sum of first 15 terms.

Answer:-

Given:

6th term of an AP = 37

We know that,

nth term of an AP (a_n) = a + (n - 1)d

→ a + (6 - 1)d = 37

→ a + 5d = 37 -- equation (1)

And also given that,

Sum of first 6 terms (S_6) = 147

Sum of first n terms of an AP = n/2 * [ a + l (nth term)]

→ 6/2 * [ a + (37) ] = 147

→ 3(a + 37) = 147

→ 3a + 111 = 147

→ 3a = 147 - 111

→ 3a = 36

→ a = 36/3

→ a = 12

Substitute "a" value in equation (1).

→ 12 + 5d = 37

→ 5d = 37 - 12

→ 5d = 25

→ d = 25/5

→ d = 5

→ 15th term = 12 + (15 - 1)(5)

→ a_15 = 12 + 70

→ a_15 = 82

Sum of first 15 terms = 15/2 * [12 + 82 ]

→ S_15 = 15/2 * (94)

→ S_15 = 705

Hence, the first term of the given AP is 12 and the sum of first 15 terms is 705.