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Question

If the sum of 99 terms of AP is 198, then what is the value of the 50th term? [1 MARK]

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Solution

Concept: 0.5 Mark
Application: 0.5 Mark

Let the first term of the AP be a, and the common difference be d.
Given: Sum of 99 terms is 198
S99=198992[2a+(991)d]=198 [Sn=n2[2a+(n1)d]
2a+98d=198×299=4
a+49d=2
a+(501)d=2
a50=2 [nth term of an AP=a+(n1)d]
The 50th term is 2.

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