Question

Find the sum of the series 5+8+11..........+68 using ap

Answer 1

Answer:

let a , l & d be the first term , last term and common difference respectively

a = 5

d = 8 - 5 = 3

l = 68

first we have to find the total number of terms in this AP

thus,

$t_{n} = a + (n - 1)d\\\\68 = 5 + (n - 1)3\\\\63 = (n - 1)3\\\\n - 1 = 21\\\\n = 22$

Therefore the sum of the series of the AP is

$S_{n} =\frac{n}{2}[a + l]\\\\S_{n} = \frac{22}{2}[5 + 68]\\\\S_{n} = 11(73)\\\\S_{n} = 803$

Answer 2

Given :

Series : 5 + 8 + 11 + ...... + 68

To find :

The sum of the given series using ap .

Solution :

Let 68 be nth term of the series .

Let a$_s$ be the first term of the series that is 5 and a$_l$ be the last term of the series that is 68 .

Then ,

68 = 5 + ( n - 1 ) * ( common difference )

=> 68 = 5 + ( n - 1 ) * 3

=> 68 = 5 + 3n - 3

=> 3n = 66

=> n = 22

sum of the series = ( n /2 ) * ( a$_s$ + a$_l$ )

=>  sum of the series = ( 22 / 2 ) * ( 5 + 68 )

=> sum of the series = 11 * 73

=> sum of the series = 803

The sum of the given series using ap is 803 .