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Question

Find the number of terms in each of the following A.P.

7,13,19,,205


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Solution

Step 1. Find the common difference

The given arithmetic series is,

7,13,19,,205

We have to find the nth term of an A P.

As we know that the arithmetic progression is a sequence of numbers such that the difference d between consecutive term is a constant.

From the given,

a=7,

So the common difference is

d=13-7

d=6

Step 2. Find the number of terms

Formula to find thenth term of an A P. is,

Tn=[a+n-1×d]

Here, Tn is the nth term, a is first term, n is the number of terms in the sequence and d is a common difference.

tn=205

By using the formula, the nth term is,

205=7+n-1×6

205=6n+1

204=6n

n=34

Hence, the number of terms is 34.


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