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

Question

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

in progress 0

1. The sum of an Arithmetic series can be calculated as:

[tex] S_{n} = frac{n}{2}(2 a_{1}+(n-1)*d) [/tex]

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

So, using the values, we get:

[tex] S_{22}= frac{22}{2}(2*153+(22-1)*(-14)) n S_{22}=132[/tex]

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

2. Sum of the sequence = 132.

Step-by-step 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]

= 11x[306 – 21×14]

= 11x[306 – 294] = 11×12 = 132

Sum of 22 terms of this sequence is 132.