The sum of first and 15th term of an arithmetic sequence is 38.(a) Wha

1.	The sum of first and 15th term of an arithmetic sequence is 38.(a) What is the sum of 7th and 9th term ?
Answer» The sum of 7TH and 9th TERM is 369. Explanation: Given: sum of first and 15th term = 38 Sum of 7th and 8th term = ? A.P can be written as a, a + d, a + 2d… a + (n – 1)d Let first term = a 15th term = a + (15 – 1)d = a + 14d a + a + 14d = 38 2a + 14d = 38 2(a + 7d) = 38 a + 7d = 38/2 a + 7d = 19 ------(1) [8th term] Therefore, Sum of 7th and 9th term = a + 6d + a + 8d = 19 Common difference, d = 19. Sum of arithmetic series, sₙ = $\frac{n}{2}$ [a + a + 14d] {first and last term} 38 = $\frac{15}{2}$ [2a + 14 x 19] 38 = 7.5[2a + 266] 38 = 15a + 1995 a = -51.5 So, Sum of 7th and 9th term = 2a + 14d = 2 x -51.5 + 14 x 19 = 369 The sum of 7th and 9th term is 369. To KNOW more: The sum of the 2nd term and the 7th term of an AP is 30. If its 15th ... brainly.in/question/1467425 The sum of the THIRD and the seventh terms of an Ap is 6 and their ... brainly.in/question/50894

The sum of first and 15th term of an arithmetic sequence is 38.(a) What is the sum of 7th and 9th term ?

Answer»

Explanation:

Given: sum of first and 15th term = 38

Sum of 7th and 8th term = ?

A.P can be written as a, a + d, a + 2d… a + (n – 1)d

Let first term = a

15th term = a + (15 – 1)d = a + 14d

a + a + 14d = 38

2a + 14d = 38

2(a + 7d) = 38

a + 7d = 38/2

a + 7d = 19 ------(1) [8th term]

Therefore,

Sum of 7th and 9th term = a + 6d + a + 8d = 19

Common difference, d = 19.

Sum of arithmetic series, sₙ = $\frac{n}{2}$ [a + a + 14d] {first and last term}

38 = $\frac{15}{2}$ [2a + 14 x 19]

38 = 7.5[2a + 266]

38 = 15a + 1995

a = -51.5

So, Sum of 7th and 9th term = 2a + 14d

= 2 x -51.5 + 14 x 19

= 369

The sum of 7th and 9th term is 369.

To KNOW more:

The sum of the 2nd term and the 7th term of an AP is 30. If its 15th ...

The sum of the THIRD and the seventh terms of an Ap is 6 and their ...