sequences and series (1 Viewer)

[fashionista]

hi fellooows

grr theres this sequences and series question for 2 u that i was hoping some one cud help me wit pleez
it goes
3 numbers form an arithmatic sequence and sum up to give 24. when 1,1 and 13 are added to each of them respectively they give a geometric sequence. Find the two sequences( assume the first three terms to be a,a+d, a+2d)
thank u thank u!!:wave:

 

[-=«MÄLÅÇhïtÊ»=-]

a, a+d, a+2d forms AP that adds up to 24
ie. a + a+d + a+2d = 24
3a + 3d = 24
a + d = 8

a+1, a+d+1, a+2d+13 forms a GP
ie.
(a+d+1) / (a+1) = (a+2d+13) / (a+d+1)
expand and then use the relation that a+d = 8 to get everything in terms of a. You'll end up with a quadratic looking like
a^2 - 28a + 52 = 0
(a - 26)(a - 2) = 0
therefore a = 2 or 26

since the sum of AP is only 24, a cannot be 26. Therefore a = 2.

a+d=8, therefore d=6
So the AP is 2, 8, 14
GP is 3, 9, 27

 

[fashionista]

than u thank u thank u!!!