Question

Sum of the first 9 terms of an arithmetic sequence is 108. What is the fifth term?​

Answer 1

Given:

The first 9 terms of the arithmetic sequence is 108

To find:

Here, we need to find the fifth term.

Solution:

• The A.P can be listed with 9 terms.
• The center can be named as 'a'
• The difference can be defined as 'd'

The terms are as

The left sides are negative sides

(a - 4 d), (a - 3 d), (a - 2 d)  (a - d)

The right sides are positive sides    

a, (a +d), (a +2d), (a +3d)  (a +4d)

Now we will join the terms

(a - 4 d), (a - 3 d), (a - 2 d)  (a - d) a, (a +d), (a +2d), (a +3d)  (a +4d)

Now, we can sum the series

(a - 4 d)+ (a - 3 d)+ (a - 2 d) + (a - d) + a+ (a +d)+ (a +2d)+ (a +3d) + (a +4d) = 108

= 9a = 108  

a = 12.

The fifth term of the Arithmetic sequence is 12.

Answer 2

Answer:

Sum of the first 9 terms of an arithmetic sequence is 108. What is the fifth term? What is the sum of first term and ninth term?