First slide

Arithmetic progression

Question

If sum of four numbers in A.P. is 28 and product of two middle terms is 45, then product of the first and last terms is

Moderate

A

11
B

13
C

15
D

17

Solution

Let four numbers in A.P. be
$a - 3 d, a - d, a + d, a + 3 d$
We are given
$\begin{array}{l} 28 = (a - 3 d) + (a - d) + (a + d) + (a + 3 d) = 4 a \\ \Rightarrow a = 7 \end{array}$
Also, $(a - d) (a + d) = 45$
$\Rightarrow 49 - d^{2} = 45 \Rightarrow d = \pm 2 .$
Now, $(a - 3 d) (a + 3 d) = a^{2} - 9 d^{2} = 13$

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