Question
In an arithmetic progression, the first term is 18, the
common difference is 6, and the total number of terms is 48. What is the sum of all the terms in this series?Solution
First term (a) = 18
Common difference (d) = 6
Number of terms (n) = 48
Required sum = (n/2){2a + (n – 1) × d}
= (48/2) × {2 × 18 + (48 – 1) × 6}
= 24 Ă— (36 + 47 Ă— 6) = 24 Ă— (36 + 282)
= 24 Ă— 318 = 7632
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