Question

Find the 15th term of an arithmetic progression whose first term is 2 and the common difference is 3

Answer 1

Tip: An arithmetic progression is a series in which the difference between the consecutive numbers is the same.

The equation of an AP is $a_n=a+(n-1)d$ where $a$ is the first term, $n$ is the number of terms, $d$ is the common difference, $a_n$ is the $n^{th}$ term

Given:

$a=2$ and $d=3$

To find: $a_{15}$

Explanation:

To find the $n^{th}$ term, $a_n=a+(n-1)d$

$\implies a_{15}=2+(15-1)3$

$\implies a_{15}=2+(14)3$

$\implies a_{15}=2+42$

$\implies a_{15}=44$

The $15^{th$ term of the series is $44$

Answer 2

Given,

The first term of an arithmetic progression is 2 and the common difference is 3.

To Find,

The 15th term =?

Solution,

We can solve the question as follows:

It is given that the first term of an arithmetic progression is 2 and the common difference is 3. We have to find the 15th term.

$First\: term = 2$

$Common\: difference =3$

$n = 15$

The nth term of an arithmetic progression is given as:

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

Where,

$a = First\: term$

$d = Common\: difference$

$n = nth\: term$

Substituting the values in the above formula,

$T_{15} = 2 + (15 - 1)3$

     $= 2 + 14*3$

     $= 2 + 42$

     $= 44$

Hence, the 15th term is equal to 44.