Question

the sum of the 3 nos in ap is 18 if the prod of first and the third term is 5 times tge common difference find the 3 nos​

Answer 1

s3=3\2(a+2d)

18=3\2×2(a+d)

18\3=a+d

a+d=6

a=6-d

a(a3)=5d

a(a+2d)=5d

(6-d)(6-d+2d)=5d

(6-d)(6+d)=5d

(6^2-d^2)=5d

36-d^2=5d

5d+d^2-36=0

d^2+5d-36=0

d^2+9d-4d-36=0

d(d+9)-4(d+9)=0

(d+9)(d-4)=0

d=-9 or d=4

if d=4

a=6-4

Ap→2,6,10

if d=-9

a=6-(-9)=15

Ap→15,6,-3

Answer 2

Answer:

Step-by-step explanation:

assume the no.s to be (a-d),a,(a+d)

(a-d)+a+(a+d)=18

3a=18

a=6 ......................(1)

product: (a-d)(a+d)=5d

a^2-d^2=5d

36-d^2=5d

d^2+5d-36=0

by splitting middle term,

(d+9)(d-4)=0

thus, d=4 or -9

with d=4 : solutions 2,6,10

with d=(-9) : solutions 15,6,-3