Question

The sum of the first three terms of an AP is 165, and the sum of the next three terms is 309. What is the value of the 9th term?

• A. 183
• B. 167
• C. 231
• D. 151

Answer 1

The correct option is A 183

let the first three terms be a, a+d and a-d
a + ( a+d) + ( a – d) = 165
3a = 165
a = 55
let the next three terms be ,
a+d, a + 2d and a+ 3d
a + a+2d + a+3d = 309
3a + 9d = 309
a + 3d = 103
substitute a in above equation to get the value of d
55 + 3d = 103
3d = 103 – 55
d = 48/3 = 16
T9 = a+ (n-1) * d
T9 = 55 + (9-1) * 16 = 55 + 8 *16 = 183