Question

The 14th term of an A.P. is twice its 8th term. If the 6th term is -8, then find the sum of its first 20 terms.

Answer 1

Step-by-step explanation:

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Answer 2

Answer:S20= -340

Step-by-step explanation:

T14=2T8. According the question

a+(14-1)d = 2(a+(8-1)d)

a+13d = 2(a+7d)

a+13d = 2a+14d

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

a+d=0

a= -d

And

d = -a

We know that

T6 = -8

a+(6-1)d = -8

a+5d =-8

Put the value of a

-d+5d = -8

4d= -8

d= -2

So a= -(-2) = 2

Find the S20

S20 = 20/2 (2×a+ (20-1)d)

= 10 (2×2 + (19)-2)

= 10 (4 +(-38))

= 10 (4 -38)

= 10(-34)

= -340