Question

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The 14th term of an AP is twice its 8th term. If its 6th term is -8 then find the sum of its

first 20 terms.​

Answer 1

Answer:

According to the question

14th term = 2× 8th term

a+13d= 2×(a+7d) => a+13d=2a+14d

a+13d-2a-14d=0

-a-d=0

a+d=0.......१

6th term =a+5d= -8 (given).......२

form eq १ d= -a

put d in a+5d= -8

a -5a = -8

- 4a = -8

a=2

put again a=2 in a+d=0

2+d=0

d= -2

now we have a=2 , d= -2 , n= 20

we have to find the sum of its first 20 terms.

S = n/2 {2a+(n-1)d}

S= 20/2 {2×2 + (20-1) -2}

S= 10 {4 + 19× -2}

S= 10 (4 - 38)

S = -340