the 5th term of a geometric sequence is 144 and the 10th term is 4608. find the first term and common difference

First term = 9.

Common ratio = 2.

Step-by-step explanation:

A geometric sequence has a common ratio r.

If the first term is a:

10th term = ar^9 and 5th term is ar^4

so 1th term / 5th term = r^5

So 4608/144 = r^5

r^5 = 32

so r = 2.

Substituting for r in the 5th term:

a(2)^4 = 144

a = 144 / 16

a = 9.

first term:9

common ratio: 2

Step-by-step explanation:

aₙ = a₁*rⁿ⁻¹

a₅ = a₁*r⁵⁻¹ = a₁*r⁴ = 144  ... (1)

a₁₀ = a₁*r¹⁰⁻¹ = a₁*r⁹ = 4608  ... (2)

(2)÷(1)  r⁵ = 32

r = 2

a₁ = 144 / 2⁴ = 9

option 1 is correct.

step-by-step explanation:

y varies inversely with x and constant of variation is 4

the equation will be:

y = k/x

where k =4 so,

y = 4/x

if we put values of x of option 1 in the above equation and find values of y

y = 4/-2 => y =-2

y = 4/-1 => y = -4

y = 4/1 => y = 4

y = 4/2 => y =2

so, all the values of x and y are correct.

if we put values of x given in other options and find value of y we cannot find whole table satisfying the equation.

hence option 1 is correct.