Question

Q. The first term of an ap is -1 and the last term is 45 . If the sum of the terms of the ap is 120 , then find the number of terms and common difference ?​

Answer 1

The first term of an ap is -1 and the last term is 45. If the sum of the terms of the ap is 220, then find the number of terms and common difference?​ [ correct question]

Given:

The first term of an ap is -1 and the last term is 45 if the sum of the terms of the ap is 120

To find:

The number of the terms and common difference

Solution:

We have given the case of the arithmetic progression

where the sum of the terms is given by:

$S = \frac{n}{2}(a+l)$

where

s is the sum of the terms

n is the number of the terms

a is the first term

l is the last term

now putting the value of the given terms

$220 = \frac{n}{2}(-1+45)$

$220 = \frac{n}{2}44$

$220 = 22n$

n = 10

and the value of the nth can be calculated by

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

$45 = -1+(10-1)d$

$46 = 9d$

$d = \frac{46}{9}$

The number of the terms and the common difference is 10  and 46/9