Question

how many terms are there in A.P. 201,208,215,................,369?

Answer 1

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24


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Answer 2

Let the number of terms be n, it means let there are n terms.

First term = a

                 = 201

Common Difference = d

                 = any term - previous term

                 = 215 - 208 = 208 - 201

                 = 7

Last term = n th term

                = $a_{n}$

                = 369

We know,

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

369 = 201 + ( n - 1 )( 7 )

369 - 201 = ( n - 1 ) 7

168 = ( n - 1 )7

168 / 7 = n - 1

24 = n - 1

24 + 1 = n

25 = n

Therefore,

Number of the terms present between the given AP is 25.