Question

The sum of first three terms of an ap is 18. If the product of the first and the third term is 5 times the common difference find the three numbers

Answer 1

Step-by-step explanation:

Let the three terms be a,b,c

In anA.P terms are in the form a,a+d,a+2d,a+3d,...

Now, a+b+c=18

=>> a+a+d+a+2d = 18

=>> 3a+3d = 18

=>> a+d = 6-----(1)

Therefore 2nd term is 6

a×(a+2d) = 5d

substituting (d=6-a ) from equation (1)

a×[a+2(6-a)] = 5(6-a)

a×[a+12-2a] = 30-5a

a×[12-a] = 30-5a

-a^2+12a=30-5a

a^2-5a-12a+30=0

a^2-17a+30=0

a^2-2a-15a+30=0

a(a-2)-15(a-2) = 0

(a-15)(a-2) = 0

a=15 or a=2

we take a=2

Therefore first term is a=2

Substituting a=2 in equation (1)

a+d=6

=>>2+d =6

=>>d=4

Third term = a+2d

= 2+2(4)

= 2+8

= 10

Hence the three terms a,b,c are 2,6,10