Q. If the sum of two extreme numbers of an AP with four terms is 8 and product of remaining two middle terms is 15, then greatest number of the series will be
A) 5
B) 7
C) 9
D) 11
Explanation
(b)
Let four numbers are $a - 3d,\ a - d,\ a + d,\ a + 3d.$
$\therefore(a - 3d) + (a + 3d) = 8$
$\Rightarrow (a - d)(a + d) = 15$
and $(a - d)(a + d) = 15$
$\Rightarrow \ a^{2} - d^{2} = 15$
$\Rightarrow d = 1$
Thus, required numbers are 1, 3, 5, 7 .
Hence, greatest number is 7.
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.