Question

How is the sum expressed in sigma notation? 22 + 27 + 32 + 37 + 42 + 47

Answer 1

The sum expressed in sigma notation is $\sum_{n=1}^{6} 5 n+17$.

Solution:

Given series is 22 + 27 + 32 + 37 + 42 + 47.

Write it in the sequence form 22, 27, 32, 37, 42, 47.

First term of the sequence = 22

Common difference = 27 – 22 = 5

This is arithmetic sequence.

$\text n^{th}$ term of the arithmetic sequence is

$a_n=a_1+(n-1)d$

$\Rightarrow a_n=22+(n-1)5$

$\Rightarrow a_n=22+5n-5$

$\Rightarrow a_n=17+5n$

$\Rightarrow a_n=5n+17$

In the given series number of terms is 6.

So n = 1 to 6.

Write n = 1 in the lower of the sigma and 6 in the top of the sigma.

$\sum_{n=1}^{6} 5 n+17$

The sum expressed in sigma notation is $\sum_{n=1}^{6} 5 n+17$.