MATH SOLVE

4 months ago

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

Accepted Solution

A:

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)) \\ \\ S_{22}=132[/tex]

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

[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)) \\ \\ S_{22}=132[/tex]

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