Question

find the nth term and 13th term of the A.P 7,10,13.....​

Answer 1

The given Arithmetic Progression is as follows :-

7,10,13.....

$\rule{200}{2}$

The first Term of the AP is denoted by 'a'.

Hence,

a = 7

The common difference is denoted by 'd'.

Hence,

d = 10-7 = 3

$\rule{200}{2}$

Now,

We know that :-

$a_n =a +(n-1)d$

Hence ,

nth term of the AP given will be :-

$= 7 + (n - 1)3 \\ \\ \\ = 7 + 3n - 3 \\ \\ \\ = 4 + 3n$

$\rule{200}{2}$

For finding 13th term, we have 2 ways :-

Way 1 :-

Given that :-

nth term of AP is 4+3n

So,

13th term will be equal to :-

$= 4 + 3n \\ \\ = 4 + 3(13) \\ \\ \\ = 4 + 39 \\ \\ = 43$

Way 2 :-

We know that :-

nth term an AP is given by a +(n-1)d

So,

13 th term Will be :-

$= 7 + (13 - 1)3 \\ \\ \\ = 7 + 12(3) \\ \\ = 7 + 36 \\ \\ = 43$

$\rule{200}{2}$

Thus,

nth term = 4+3n

13th term = 43

$\rule{200}{2}$

Answer 2

Step-by-step explanation:

The given Arithmetic Progression is as follows :-

7,10,13.....

The first Term of the AP is denoted by 'a'.

Hence,

a = 7

The common difference is denoted by 'd'.

Hence,

d = 10-7 = 3

Now,

We know that :-

a_n =a +(n-1)da

n

=a+(n−1)d

Hence ,

nth term of the AP given will be :-

$\begin{lgathered}= 7 + (n - 1)3 \\ \\ \\ = 7 + 3n - 3 \\ \\ \\ = 4 + 3n\end{lgathered}$

For finding 13th term, we have 2 ways :-

Way 1 :-

Given that :-

nth term of AP is 4+3n

So,

13th term will be equal to :-

$\begin{lgathered}= 4 + 3n \\ \\ = 4 + 3(13) \\ \\ \\ = 4 + 39 \\ \\ = 43\end{lgathered}$

Way 2 :-

We know that :-

nth term an AP is given by a +(n-1)d

So,

13 th term Will be :-

$\begin{lgathered}= 7 + (13 - 1)3 \\ \\ \\ = 7 + 12(3) \\ \\ = 7 + 36 \\ \\ = 43\end{lgathered}$

Thus,

nth term = 4+3n

13th term = 43