Question

Four numbers are given. The first three numbers are terms of a geometric sequence and the last three numbers are terms of an arithmetic sequence. The sum of the first and the last number is and the sum of the middle two numbers is . Find those numbers?

Answer 1

Answer:

example:

First three terms of geometric sequence =x,y,z

sum of the three terms=42

the three terms of the geometric sequence with the common ratio r will be=x,xr,xr

2

=42

on multiplying the middle term by 4,5

we will get the arithmetic sequence as- 4,5

xr-x=xr 2-45 xr

therefore, 2r 2 -5r+2=0

r=21,2

on substituting the values in the equation x+xr+xr2

=42, we will get

x=6 or 24

thus the largest value of x=24