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

1.	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» 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.

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»

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.

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

Substitute "a" value in equation (1).

→ 12 + 5d = 37

→ 5d = 37 - 12

→ 5d = 25

→ d = 25/5

→ 15TH term = 12 + (15 - 1)(5)

→ a_15 = 12 + 70

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

→ S_15 = 15/2 * (94)

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