Question

Find the 24th term of the arithmetic sequence 11, 14, 17, … . Express the 24 terms of the series of this sequence using sigma notation. Find the sum of the first 24 terms of the series.

Answer 1

Answer:

The 24th term is 80 and the sum of 24 terms is 1092.

Explanation:

Given that,

The arithmetic series is

11,14,17,........24

First term a = 11

Difference d = 14-11=3

We need to calculate the 24th term of the arithmetic sequence

Using formula of number of terms

$t_{n}=a+(n-1)d$

Put the value into the formula

$t_{24}=11+(24-1)\times3$

$t_{24}=80$

$t_{24}=u_{24}=80$

We need to calculate the sum of the first 24 terms of the series

Using formula of sum,

$S_{n}=\dfrac{n}{2}(a+u_{24})$

Put the value into the formula

$S_{n}=\dfrac{24}{2}\times(11+80)$

$S_{n}=1092$

Hence, The 24th term is 80 and the sum of 24 terms is 1092.