Question

How many terms of the sequence -2 3 8 13... will make the sum 568?

Answer 1

Given :  sequence -2 3 8 13.

To Find :  How many terms of the sequence  will make sum 568

Solution:

sequence -2 3 8 13.

a = - 2

d = 3 -(-2) = 5

n = term

Sum = (n/2)(2a + (n -1)d)

sum = 568

=> (n/2)(2*(-2) + (n-1)5) = 568

=> n(-4 + 5n - 5) = 1136

=> n(5n - 9) = 1136

=> 5n² - 9n  = 1136

=> 5n² - 9n - 1136 = 0

=> 5n² - 80n + 71n - 1136 = 0

=> 5n(n - 16) + 71(n - 16) = 0

=> (n - 16)(5n + 71) = 0

=> n = 16    , n = -71/5 ( which is not possible)

Hence n = 16

16 terms will make sum 568

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