Question

find the sum of the following series 2+5+8+...upto 31 terms

Answer 1

2 + ( ( 31 - 1 ) * 3 ) = 92

Answer 2

Given,

The following series: 2+5+8+     upto 31 terms.

To Find,

The sum of the series =?

Solution,

We can solve the question as follows:

We have to find the sum of the given series up to 31 terms. Let us check if the given terms are in arithmetic progression or not. A series of numbers are in A.P. is the difference between two consecutive terms is constant.

Here,

$5 - 2 = 3\\8 - 5 = 3$

Since the difference between the terms is constant, the series is in A.P.

We know that the sum of n terms in an A.P. is given as:

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

Where,

$n = Number\:of\: terms\\a = First\: term\\d = Common\: difference$

From the given series,

$n = 31\\a = 2\\d = 3$

Substituting the values in the above formula,

$S_{n} = \frac{31}{2} (2*2 + (31-1)3)$

    $= \frac{31}{2}(4 + 30*3)$

    $= \frac{31}{2}* 94$

    $= 1457$

Hence, the sum up to 31 terms is 1457.