Question

The 14 term of an ap is twice its 18 term its 8 term if its 6 term is -8 then find the sum of first 20 terms

Answer 1

Answer:

20

Step-by-step explanation:

2(a+13d) = a+17d (Given)

2a + 26d = a + 17d

a = 17d - 26d

a = -9d              ...(1)

a + 5d = -8 (Given)

From (1),

-9d + 5d = -8

-4d = -8

d = 2             ...(2)

Substituting (2) in a + 5d = -8, we get

a + 10 = -8

a = -18            ...(3)

Now, the values we have obtained are:

a = -18

d = 2

n = 20 (For summation)

Summation formula : n/2{2a + (n - 1)d}

Substituting (2) and (3) in the formula, we get:

20/2 {-36 + (20 - 1)2}

10(-36 + 38)

10(2)

=20

Therefore the sum of its first 20 terms is 20.