First slide

Arithmetic progression

Question

Five numbers are in A.P. whose sum is 25 and product is 2520, if one of these five numbers is $- \frac{1}{2}$ , then the greatest number amongst them is

Moderate

A

$\frac{21}{2}$
B

16
C

27
D

7

Solution

Let terms be $a - 2 d, a - d, a, a + d, a + 2 d$
Sum = $25 \Rightarrow 5 a = 25 \Rightarrow a = 5$
Also product = 2520 $\Rightarrow (5 - 2 d) (5 - d) 5 (5 + d) (5 + d) = 2520$
$\Rightarrow (25 - 4 d^{2}) (25 - d^{2}) = 504$
$\Rightarrow 625 - 100 d^{2} - 25 d^{2} + 4 d^{4} = 504$
$\Rightarrow 4 d^{4} - 125 d^{2} + 625 - 504 = 0$
$\Rightarrow 4 d^{4} - 125 d^{2} + 121 = 0$
$\Rightarrow (d^{2} - 1) (4 d^{2} - 121) = 0$
$\Rightarrow d = \pm 1, d = \pm \frac{11}{2}$
$d = \pm 1$ is not possible since one of the terms is $- \frac{1}{2}$
$\Rightarrow d = \frac{11}{2}$
$∴$ Largest term = 5+ 2d = 5 + 11 = 16

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App