Question

Find first term of a gp is 1 . The sum of the third and figth term is 90. Find the common ratio of the gp

Answer 1

Answer:

common ratio  = ± 3

in imaginary ±3.162$\iota$

Step-by-step explanation:

Let say terms of GP are

1  , r  , r² ,  r³  , r⁴

r² + r⁴ = 90

r²(r²+1) = 90

let say r² = a

a(a+1) = 90

a² + a -90 = 0

a² + 10a - 9a - 90 = 0

a(a+10) -9(a+10) = 0

(a + 10)(a-9) = 0

a = 9 or a = -10

r² = 9

r = ±3

r² = -10

r = ±(√10)$\iota$

r = ±3.162$\iota$

Answer 2

Answer:

Step-by-step explanation:

A=1

An=A(R^n-1)

A3+A5=90

1(R^2+R^4) =90

R^4+R^2-90=0

Let X=R^2

X^2+X-90=0

Solving the equation,

X=9/-10 Neglecting imaginary value

R=+/-3