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Question

An arithmetic sequence has its 5th term equal to 22 and its 15th term equal to 62. Find the 100th term


A

400

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B

402

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C

401

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D

302

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Solution

The correct option is B

402


: a5 = a + ( 5 – 1 )d = 22 ------------ ( i )

a15 = a + (15 – 1)d = 62 ------------------- (ii)

(ii) – (i) 62 – 22 = 14d – 4d = 10d

d = 4

Now, a + ( 5 – 1 )4 = 22

a = 6

Now, a100 = 6 + (100 – 1)4 = 402


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