Question

The first and last terms of an arithmetic progression are 32 and ­43. if the sum of the series is ­88, then it has how many terms?

Answer 1

Sn= n/2(a+l)
88=n/2(32+43)
176=75n
n=176/75
but value of n can't be in fraction.since domain of sequence is always natural number.

Answer 2

Answer:

It can't be possible as n is not in fraction.

Approx 2 terms.

Step-by-step explanation:

Given : The first and last terms of an arithmetic progression are 32 and ­43. if the sum of the series is ­88.

To find : How many terms in the series?

Solution :

The formula of sum of series is

$S_n=\frac{n}{2}[a+l]$

Where $S_n$ is the sum of n terms, $S_n=88$

a is the first term, a=32

l is the last term l=43

and n is the number of terms

Substituting the value,

$88=\frac{n}{2}[32+43]$

$88\times 2=n[75]$

$176=75n$

$n=\frac{176}{75}$

$n=2.3$

But value of n can't be in fraction as the domain of sequence is always natural number.

So, Approximately there are 2 terms.