Three numbers are in a.p.and their sum is 15.if 1,4 and 19 be added to those numbers respectively.the numbers are in g.p find the numbers
Answers
Step-by-step explanation:
let the numbers be a1,a2,a3 and the common difference be d
a1 = a2 - d
a3 = a2 + d
According to the given problem,
a1 + a2 + a3 = 15
=> (a2 - d) + a2 + (a2 + d) = 15
=> 3 * a2 = 15
=> a2 = 5
now second part,
According to the question,
(a2 - d + 1), (a2 + 4), (a2 + d + 19) are in G.P.
therefore,
=> (a2 + 4) / (a2 - d + 1) = (a2 + d + 19) / (a2 + 4)
=> (a2 + 4)^2 = (a2 - d + 1) (a2 + d + 19)
=> 9^2 = (6 - d) (24 + d)
=> 81 = 144 + 6d - 24d - d^2
=> d^2 - 18d + 63 =0
=> d^2 + 21d - 3d + 63 = 0
=> d (d + 21) - 3 (d + 21) = 0
=> (d + 21) (d - 3) = 0
=> d + 21 = 0 or d - 3 = 0
=> d = -21 or d = 3
if d = -21 the a1 = 5 - (-21)
= 5 +21
= 26
if d = 3 the a1 = 5 - 3
= 2
Done!!!!!!