Question

If in an AP S,= 256, a= 1 and d= 2, then the value of n will be​

Answer 1

Answer:

• Number of terms = n = 16

Explanation:

Given:

• An A.P. in which:

1. Sum of the numbers = $S_{n}$ = 256
2. First term = a = 1
3. Common difference = d= 2

To find:

The number of terms = n

Proof:

According to the question,

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

Substituting

1. $S_{n}$ = 256
2. a = 1
3. d = 2

in the above equation, we get:

=  256 = $\frac{n}{2} [2(1) + (n-1) X 2 ]$

⇒  256 = $\frac{n}{2} [2 + (2n -2) ]$

⇒  256 = $\frac{n}{2} [2n ]$

⇒  256 = $n^{2}$

⇒ $n^{2}$ =  256

⇒ n = $\sqrt{256}$

⇒ n = ± 16

Hence, the number of terms = n =  ± 16  

But, the number of terms cannot be negative.

∴ Number of terms = n = 16

Hence, proved.

Hope you got that.

Thank You.