Question

the sum of the first three numbers in an arithmetic progression is 18 if the product of the first and the third term is 5 times the common difference find the three numbers ​

Answer 1

this is the a.p

hope it helps...

Answer 2

Answer:

Step-by-step explanation

ACCORDING TO THE QUESTION

SUM OF FIRST THREE OF THE A.P IS 18

SO

a1+a2+a3=18

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

3a+3d=18

DIVIDING BY 3

a+d=6

a=6-d—(1)

ACCORDING TO THE QUESTION

a(a+2d)=5d

SUBSTITUTING THE VALUE OF a

a2+2ad=5d

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

36-12d+d2+ 2(6d-d2)=5d

36-12d +d2 +12d-2d2=5d

36–d2=5d

d2+ 5d-36=0

USING FACTORISATION

d2+9d–4d–36=0

d(d+9)-4(d+9)

(d-4)(d+9)

d=4 or d=–9

CASE I

WHEN d=4

a=6-d

a=6-4

a=2

NUMBERS =2,6,10

CASE II

WHEN d=–9

a=6–(–9)

a=6+9

a=15

NOW THE NUMBERS ARE

15,6,–3