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the three terms are 2,6,10.
Step-by-step explanation:
Let three three numbers in an AP are a-d, a,a+d. Where d is common difference.
It is given that the sum of the first three numbers in an AP is 18.
(a-d)+a+(a+d)=18
3a=18
a=6
The product of first and third term is 5 times the common difference.
(a-d)(a+d)=5d
a^2-d^2=5d
(6)^2-d^2=5d
d^2+5d-36=0
d^2+9d-4d-36=0
d(d+9)-4(d+9)=0
(d-4)(d+9)=0
d=4,-9
If a=6 and d =4, then the three terms are 2,6,10.
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