Sequence be like
Algebra
Level
3
The first, fourth, and eighth terms of a nonconstant arithmetic sequence form a geometric sequence. If its twentieth term is 56, what is its tenth term?
The answer is 36.
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1 solution
let first term = x common difference = y so second term = x+y third = x+2y fourth = x+3y... now first, fourth and eighth term are in GP so (x+3y) / x = (x+7y) / (x+3y) from here x = 9y
now 20th term = 56 x + 19y= 56 9y + 19y = 56 28y = 56 y = 2
now 10th term = x + 9y = 9y +9y = 18y = 18*2 = 36