Q. 354.0( 6 Votes )

An AP 8, 10, 12, ... has 60 terms. Find its last term. Hence, find the sum of its last 10 terms.

Answer :

Here, First term = a = 8

Common difference = d = 10 - 8 = 2


No. of terms = 60


last term will be 60th term.


Using the formula for finding nth term of an A.P.,


l = a60 = a + (60 - 1) × d


l = 8 + (60 - 1) × 2


l = 8 + 118 = 126


Now, sum of last 10 terms = sum of first 60 terms - sum of first 50 terms


i.e. sum of last 10 terms = S60 - S50


Now, Sum of first n terms of an AP is


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


Sum of first 50 terms is given by:


S50 = [2(8) + (50 - 1)(2)]


= 25 × [16 + 98]


= 25 × 114


= 2850


Now, Sum of first 60 terms is given by:


S60 = [2(8) + (60 - 1)(2)]


= 30 × [16 + 118]


= 30 × 248


= 4020


Now, S60 - S50 = 4020 - 2850


= 1170


last term = 126, sum of last 10 terms = 1170


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