Question

find three consecutive natural number whose sum is 26

Answer 1

take a number as x

then the other numbers will be x+1 and x+2

so the statement will be:

x+x+1+x+2=26

3x+3=26

x=29/3

Answer 2

Let a/2, a, ar be the three consecutive numbers in G.P. THEN

a/2 + a + ar = 26 …(1)

And (a/2)×(a)×(ar) = 216 …(2)

From (2), we get a×a×a = 216, that is a = 6

Substituting a = 6 in (1) ,we have

6/r +6r +6= 26

6( 1/r + r ) = 20

1+r = 10/3r

3r×r - 10r + 3 = 0

This quadratic in r, solving, we get

r = 3 or 1/3 (neglecting 1/3)

r = 3.

Thus, the three consecutive numbers are:

2, 6, 18, which are in G.P.