Suppose the nth term of a series is 1 n 2 n2 2 If there are 20 terms in the series then th...........

Quantitative Aptitude( Paper-I ) Number System

Suppose the nth term of a series is 1 + n/2 + n²/2

If there are 20 terms in the series, then the sum of the series is equal to

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CAPF 2021 Paper-1

1360

1450

1500

1560

- The given nth term of the series is: Tn = 1 + n/2 + n²/2.

- To find the sum of this series with 20 terms, calculate each component separately.

- The constant term 1 is added 20 times, contributing 20 to the sum.

- For n/2 over 20 terms (from 1 to 20), the sum is (1/2)(1 + 2 + ... + 20) = (1/2)(20)(21)/2 = 105.

- For n²/2 over 20 terms, the sum is (1/2)(1² + 2² + ... + 20²).

- Sum of squares 1² to 20² is (20)(21)(41)/6 = 2870.

- Thus, the sum for n²/2 is (1/2)(2870) = 1435.

- Total sum of the series = 20 + 105 + 1435 = 1560.

Correct Option: Option 4, 1560

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