Question

find the sum of the following series 10 + 14 + 18 + 22 + ................ + 104

Answer 1

sum = (a1+an)*n/2

an = a1+(n-1)d
104 = 10 + (n-1)4
94 = (n-1)*4
49 = (n-1)*2

So, n - 1 = 49/2

But n (number of terms) has to be an integer.

Hence the question is wrong or the final term is not 104

Answer 2

Given:

Series 10 + 14 + 18 + 22 + ................ + 114.

To Find:

Sum of series

Solution:

From the above series, it can be seen that,

The difference between consecutive numbers is 4.

10↔1 4 = 4

14↔ 18 = 4 and so on

hence the above series is an arithmetic progression with

first term ( a )= 10,

common difference ( d ) = 4

and last term ( l ) = 104

the general term of A.P. is Tₙ = a + (n-1)d

so,

114 = 10 + ( n-1) 4

( 114 -10 )/4 = n-1

26 = n-1

27 = n

so 114 is 27th term

The Sum of A.P. is given by,

Sₙ = n/2 × [a + l ]

where,

a is the first term,

l is the last term.

So, the sum of the series is:

⇒ n/2 × ( 10 + 114 )

⇒ 27 / 2 × 124

⇒ 1674

Hence, the sum of the series is 1674.