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.
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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
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