Question

If the first term of the series is 30 and the 14th term is 95, what is the sum of all the terms of the series?

Answer 1

Answer:

The sum of all the terms in series is 875.

Step-by-step explanation:

Given : If the first term of the series is 30 and the 14th term is 95,

To find : What is the sum of all the terms of the series?            

Solution :

The first term of the  series is 30 i.e. a=30

The 14th term of series is 95 i.e. $a_{14}=95$

We know that in arithmetic series the 14th term is defined as

$a_{14}=a+13d$

Substitute the value of a,

$95=30+13d$

$95-30=13d$

$65=13d$

$d=\frac{65}{13}$

$d=5$

The common difference is 5.

The sum of the series is given by,

$S_{n}=\frac{n}{2}[2a+(n-1)d]$

$S_{14}=\frac{14}{2}[2(30)+(14-1)5]$

$S_{14}=7[60+(13)5]$

$S_{14}=7[60+65]$

$S_{14}=7[125]$

$S_{14}=875$

Therefore, The sum of all the terms in series is 875.

Answer 2

Answer:

D)  $S_{14} = 875$.

Step-by-step explanation:

Given  : If the first term of the series is 30 and the 14th term is 95,

To find : what is the sum of all the terms of the series.

Solution : We have given

First term = 30 .

14 th term = 95.

Sum of all term = $S_{n} =\frac{n(first\ term +\ last\ term)}{2}$.

Here, n = 14.

 $S_{14} =\frac{14(30 +95)}{2}$.

 $S_{14} =\frac{14(125)}{2}$.

 $S_{14} =\frac{1750}{2}$.

 $S_{14} = 875$.

Therefore, D)  $S_{14} = 875$.