Question

the sum of series 24, 20 ,16,........... is 60. the number of terms....

Answer 1

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Answer 2

Given :

The sum of series 24, 20 ,16,........... is 60.

To find :

The number of terms....

Solution:

Series: 24,20,16,....

First term = a = 24

Common difference = d = 20-24= 16-20 = -4

Formula of sum of first n terms =$S_n=\frac{n}{2}(2a+(n-1)d)$

So, $60=\frac{n}{2}(2(24)+(n-1)(-4))\\120=n(48-4n+4)\\120=52n-4n^2\\30=13n-n^2\\n^2 -13n+30=0\\n^2-10n-3n+30=0\\n(n-10)-3(n-10)=0\\(n-3)(n-10)=0\\n=3,10$

So, number of terms is 10