Find the sum of the following (ii) 102, 97, 92,… up to 27 terms.

Find the sum of the following
(ii) 102, 97, 92,… up to 27 terms.
Solution :
Number of terms (n) = 27
First term (a) = 102
Common difference (d)  = 97 - 102 = -5
Sn  = (n/2) [2a + (n - 1)d]
=  (27/2) [2(102) + (27 - 1)(-5)]
=  (27/2) [204 + 26(-5)]
=  (27/2) [204 - 130]
=  (27/2) (74)
=  27 (37)
=  999
Hence the sum of 27 terms of the given series is 999.

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