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

27
B

7
C

$\frac{21}{2}$
D

16

Solution

$Let the five terms a - 2 d, a - d, a, a + d, a + 2 d$
$SUM = 5 a = 25 \to a = 5$
$PRODUCT = (25 - 4 d^{2}) (25 - d^{2}) = 504$
$\begin{array}{l} \to d = \pm 1, d = \pm \frac{11}{2} \\ If d = \pm 1 does not give - \frac{1}{2} as a term \end{array}$
$∴ d = \frac{11}{2}$
$Largest term is 5 + 2 d = 5 + 11 = 16$

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