Question

The sum of first n terms of A.P. whose first term is an integer with common difference 2 is equal to 270.
if n> 1 then 'n' can be equal to
(A)5
(B)3
(C)15
(D)50

Answer 1

Answer:

the correct answer is 5 (I hope)

Step-by-step explanation:

As it only satisfies the following condition

cont..

5a + 25 - 5 = 270

let a be 50

250+25-5= 275-5 = 270

Hence 5 is the correct answer

Answer 2

Option (C) is the correct answer.

Given:

Common difference (d) = 2

Sum of A.P.($S_n$)  = 270

n > 1

To Find:

The value of n.

Solution:

For Finding the value of '$n$'.

The formula for the sum on '$n$' terms of an Arithmetic Progression(A.P.) is,

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

And, by applying the values,

                                   $270 = \frac{n}{2} [2a+(n-1)2]$

                 $~~~~~~~~~~~~~~~540= n[2a+2n-2]\\~~~~~~~~~~~~~~~~540= 2n^2+2an-2n\\2(n^2+na-n) = 540\\~~~~~n^2+na-n=270$

Now, By using the options given in the question.

Since, by option (C) which is 15,

            $(15)^2+15(a)-15=270\\~~~~~~~~~~~~~~~~~~~~15a = 270-210$

                                      $a=\frac{60}{15}$

                                       a = 4

Hence a comes to be 4 which is a positive integer.

So, option (C) is the correct answer.