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Three numbers in AP have sum 21 and the sum of their squares is 165. Find the numbers.

Class 10Properties and Selection of AP TermsAlgebra — Sequences

A3, 7, 11
B1, 7, 13
C5, 7, 9
D4, 7, 10

Step-by-Step Solution

a = 7. (7 - d)^{2} + 49 + (7 + d)^{2} = 3 \times 49 + 2 d^{2} = 165

, so

d^{2} = 9, d

= ±3: 4, 7, 10. (Squares: 16 + 49 + 100 = 165.)

Answer: D) 4, 7, 10

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