Sequence And Series Question 570
Question: If the sum of three consecutive terms of an A.P. is 51 and the product of last and first term is 273, then the numbers are
[MP PET 1986]
Options:
A) 21, 17, 13
B) 20,16, 12
C) 22, 18, 14
D) 24, 20, 16
Show Answer
Answer:
Correct Answer: A
Solution:
Let consecutive terms of an A.P. are $ a-d,\ a,\ a+d $ . Under given condition, $ (a-d)+a+(a+d)=51 $
$ \Rightarrow $ $ a=17 $ and $ (a-d)(a+d)=273 $
$ \Rightarrow $ $ a^{2}-d^{2}=273 $
$ \Rightarrow $ $ -d^{2}=273-289 $
$ \Rightarrow $ $ d=4 $ Hence consecutive terms are 13, 17, 21. Trick: Both conditions are satisfied by (a) $ i.e. $ 21, 17, 13.
BETA
