Question

if the sum of first n terns of an ap is 2,4,6,....is 240 ,then the value of n is

Answer 1

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Answer 2

Answer:

The number of terms are 15.      

Step-by-step explanation:

Given : If the sum of first n terns of an A.P is 2,4,6,....is 240.

To find : The value of n ?

Solution :

In an A.P 2,4,6,...

First term a=2

Common difference  = 4-2=2

Sum of n terms is $S_n=240$

Applying sum of an A.P formula,

$S_n=\frac{n}{2}[2a+(n-1)d]$

Substitute the value in the formula,

$240=\frac{n}{2}[2(2)+(n-1)2]$

$240\times 2=n[4+2n-2]$

$240\times 2=n[2n+2]$

$240\times 2=2n[n+1]$

$n^2+n-240=0$

$n^2+16n-15n-240=0$

$n(n+16)-15(n+16)=0$

$(n+16)(n-15)=0$

$n=-16,15$

Reject n=-16

So, The number of terms are 15.