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

Answer 1

n th term = a + (n-1) d
14th = a + 13 d = 2 [ 8th] = 2[ a + 7 d ]
so
a + 13 d = 2 a + 14 d
a = -d
6th = a + 5 d = -8
-d + 5 d = -8
d = -2
so a = +2
sum of first n terms = (n/2)[ 2a + (n-1)d]
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= (20/2) [ 2*2 + 19(-2)] =10 [4 - 38] = 10[-34] = -340