Q. 234.6( 13 Votes )

The first and the last terms of an AP are 17 and 350 respectively. If the common difference is 9, how many terms are there and what is their sum?

Answer :

Here, first term = a = 17

Common difference = 9


Last term = l = 350


To find: number of terms and their sum.


Let there be n terms in the AP.


Since, l= 350


350 = 17 + (n - 1)9


350 - 17 = 9n - 9


333 = 9n - 9


333 + 9 = 9n


9n = 342


n = 38


Therefore number of terms = 38


Now, Sum of n terms of this arithmetic series is given by:


Sn = [2a + (n - 1)d]


= [a + a + (n - 1)d]


= [a + l]


Therefore sum of 38 terms of this arithmetic series is given by:


S38 = [17 + 350]


= 19 × 367


= 6973


n= 38 and Sn = 6973


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