Question

The sum of first and 15th term of an arithmetic sequence is 38.

(a) What is the sum of 7th and 9th term ?​

Answer 1

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.

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