Question

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

• A. 400
• B. 402
• C. 401
• D. 302

Answer 1

The correct option is B

402

: $a_5$ = a + ( 5 – 1 )d = 22 ------------ ( i )

$a_{15}$ = a + (15 – 1)d = 62 ------------------- (ii)

Subtracting (ii) from (i) $\Rightarrow$ 62 – 22 = 14d – 4d = 10d

d = 4

Now, a + ( 5 – 1 )4 = 22

a = 6

Now, $a_{100}$ = 6 + (100 – 1)4 = 402