How many terms are there in the A.P.?$7, 10, 13, … 43$.

Given:

Given A.P. is $7, 10, 13, … 43$

To do:

We have to find the number of terms in the given A.P.

Solution:

Here,

$a_1=7, a_2=10, a_3=13$

Common difference $d=a_2-a_1=10-7=3$

Let $43$ be the nth term.

We know that,

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

Therefore,

$a_{n}=7+(n-1)(3)$

$43=7+n(3)-1(3)$

$43-7=3n-3$

$36+3=3n$

$3n=39$

$n=\frac{39}{3}$

$n=13$

Hence, there are 13 terms in the given A.P.    

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Updated on: 10-Oct-2022

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