Question

There are four numbers such that first three of them form an Arithmetic Progression and the last three form a Geometric Progression. The sum of the first and the third is 2 and that of second and fourth is 26. What is the sum of first and fourth number?

• A. $85\frac{13}{25}$
• B. $25\frac{73}{85}$
• C. 83
• D. none of these

Answer 1

The correct option is D none of these

Let a, b, c, d be four numbers such that a, b, c, are in A.P. and b, c, d are in G.P
$\begin{array}{cccc}\therefore & a+c=2b& ...\left(1\right)& \\ and& bd=c^2& ...\left(2\right)& \\ Also& a+c=2& ...\left(3\right)& \\ and& b+d=26& ...\left(4\right)& \\ \Rightarrow & b=1& & \end{array}$
from (4), d = 25
$\therefore$ from (2) c = $\pm$ 5
when c = 5, then a = - 3
when c = -5, then a = 7
Hence the four numbers are - 3, 1, 5, 25 or 7, 1, -5, 25