For the ap 10,15,20,...,195; find a) the number of terms in the ap. b) the sum of all its terms
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The concept of arithmetic progression has to be used here. The series is given to us in the question. We are asked to find the the number of terms and the sum of the terms of that series.
10, 15, 20,... , 195
a = 10
d = 5
l = 195
(a)
l = a + (n - 1)d
195 = 10 + (n - 1)5
195 - 10 = (n - 1)5
185 = (n - 1)5
185 ÷ 5 = n - 1
37 = n - 1
n = 37 + 1
n = 38
(b)
S = (n/2)(a + l)
S = (38/2)(10 + 195)
S = 19(205)
S = 3895
Hence, the number of terms in the series is 38 and the sum of the terms is 3895.
Abbreviations used:-
a → First term
d → Common difference
l → Last term
n → Number of terms
S → Sum
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