Three-consecutive-terms-of-a-G-P-are-the-3rd-5th-and-8th-term-of-an-A-P-Find-the-common-ratio-

Question Number 45422 by Tawa1 last updated on 12/Oct/18

Three consecutive terms of a G . P are the 3 rd, 5 th and 8 th term of an A . P .

Find the common ratio .

Answered by tanmay.chaudhury50@gmail.com last updated on 12/Oct/18

A + (3 - 1) D = a

A + (5 - 1) D = a r

A + (8 - 1) D = {a r}^{2}

{A + 4 D} - {A + 2 D} = a r - a

2 D = a r - a

D = \frac{a r - a}{2}

A + 2 D = a

A + a r - a = a

A = 2 a - a r

A + 7 D = {a r}^{2}

2 a - a r + 7 (\frac{a r - a}{2}) = {a r}^{2}

4 a - 2 a r + 7 a r - 7 a = 2 {a r}^{2}

4 - 2 r + 7 r - 7 - 2 r^{2} = 0

- 2 r^{2} + 5 r - 3 = 0

2 r^{2} - 5 r + 3 = 0

2 r^{2} - 2 r - 3 r + 3 = 0

2 r (r - 1) - 3 (r - 1) = 0

(r - 1) (2 r - 3) = 0

r = 1 o r r = \frac{3}{2}

Commented by Tawa1 last updated on 12/Oct/18

God bless you sir

Commented by tanmay.chaudhury50@gmail.com last updated on 13/Oct/18

G o d b l e s s a l l