Question

In an A.P. sum of three consecutive terms is 27 and their product is 504, find the terms.
( Assume that three consecutive terms in A.P. are a – d , a , a + d .)

Answer 1

Assume that three consecutive terms in A.P. are a – d , a , a + d .

It is given that,
Sum of three consecutive terms = 27
Product of three consecutive terms = 504

$$\begin{gathered} \left(a-d\right)+a+\left(a+d\right)=27 \\ \Rightarrow 3a=27 \\ \Rightarrow a=9 \end{gathered}$$

$$\begin{gathered} \left(a-d\right)\times a\times \left(a+d\right)=504 \\ \Rightarrow \left(9-d\right)\times 9\times \left(9+d\right)=504 \\ \Rightarrow 81-d^2=56 \\ \Rightarrow d^2=81-56 \\ \Rightarrow d^2=25 \\ \Rightarrow d=\pm 5 \end{gathered}$$

When d = 5,
The terms are 9, 14, 19.

When d = –5,
The terms are 9, 4, –1.