How many terms are there in the A.P. ?$7, 13, 19, …, 205$.

Given:

Given A.P. is $7, 13, 19, …, 205$.

To do:

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

Solution:

Here,

$a_1=7, a_2=13, a_3=19$

Common difference $d=a_2-a_1=13-7=6$

Let $205$ be the nth term.

We know that,

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

Therefore,

$a_{n}=7+(n-1)(6)$

$205=7+n(6)-1(6)$

$205-7=6n-6$

$198+6=6n$

$6n=204$

$n=\frac{204}{6}$

$n=34$

Hence, there are 34 terms in the given A.P.    

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Updated on: 10-Oct-2022

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