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Question
If the sum of ‘n’ terms of a series is (5n2 + 3n), then find its first five terms.
Sum
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Solution
The first term of a series is always equal to the sum of the first term (S1).
1. a1 = S1 = 5(1)2 + 3(1)
a1 = 5(1) + 3
a1 = 8
2. S2 = 5(2)2 + 3(2)
= 5(4) + 6
= 20 + 6
= 26
a2 = S2 − S1
= 26 − 8
a2 = 18
3. S3 = 5(3)2 + 3(3)
= 5(9) + 9
= 45 + 9
= 54
a3 = S3 − S2
= 54 − 26
a3 = 28
4. S4 = 5(4)2 + 3(4)
= 5(16) + 12
= 80 + 12
= 92
a4 = S4 − S3
= 92 − 54
a4 = 38
5. S5 = 5(5)2 + 3(5)
= 5(25) + 15
= 125 + 15
= 140
a5 = S5 − S4
= 140 − 92
a4 = 48
The first five terms of the series are 8, 18, 28, 38, 48.
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