Question

What is the sum of the arithmetic sequence 153, 139, 125, ..., if there are 22 terms?

Answer 1

Sum of the sequence = 132.

Explanation:

The given sequence is 153, 139, 125,.......n terms.

Sum of the arithmetic sequence will be

S = n/2[2a + (n -1)d]

where n = number of terms

a = first term of the sequence

d = common difference

for the given sequence

a = 153

n = 22

d = 139 - 153 = -14

Therefore sum of 22 terms of the sequence will be

S = (22/2)[2×153 - (22-1)14]

= 11×[306 - 21×14]

= 11×[306 - 294] = 11×12 = 132

Sum of 22 terms of this sequence is 132.

Answer 2

The sum of an Arithmetic series can be calculated as:


`S_(n) = (n)/(2)(2 a_(1)+(n-1)*d)`

n = number of terms = 22
a1 =First Term of the series = 153
d = Common Difference = 139 - 153 = -14

So, using the values, we get:


`S_(22)= (22)/(2)(2*153+(22-1)*(-14)) \\ \\ S_(22)=132`

This means, the sum of first 22 terms of the series will be 132.