Find 3 numbers in an a.P whoes sum is 15 and product is 105
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Step-by-step explanation:
Let us assume the three numbers as
a , a+d , a+2d
Given,
Sum of three terms = 15
= a+a+d+a+2d = 15
= 3a+3d = 15
= a+d = 5
ie. 2nd term = 5
Product of three terms = 105
= a(a+d)(a+2d) = 105
= a(5)(a+2d) = 105
= a(a+2d) = 21
from a+d = 5 =>> a = 5-d
= (5-d)[(5-d)+2d] = 21
= (5-d)(5+d) = 21
= 25-d^2 = 21
= d^2 = 4
= d = 2
Therefore a = 5-4 = 1
Hence terms are :
a = 1
a+d = 5
a(a+2d) = 1(a+2d) = 21
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