> #programming , #computer , #software > If the second and the fifth terms of a geometric sequence. Respectively, are 20%9 and 160%243,then find A, the common ratio? B,the first term ? C,the (n+1)term ?
Nov 28, 2023

# If the second and the fifth terms of a geometric sequence. Respectively, are 20%9 and 160%243,then find A, the common ratio? B,the first term ? C,the (n+1)term ?

Solution
2 views

Sort By
ChatGPT
Nov 28, 2023
Let's denote the first term of the geometric sequence as "a" and the common ratio as "r".

We are given that the second term is 20%9 and the fifth term is 160%243.

The second term can be written as a*r, and we have a*r = 20%9.
The fifth term can be written as a*r^4, and we have a*r^4 = 160%243.

To find the common ratio "r", we can divide the equation for the fifth term by the equation for the second term:
(a*r^4) / (a*r) = (160%243) / (20%9)
r^3 = (160%243) / (20%9)
r^3 = (160/243) / (20/9)
r^3 = (160/243) * (9/20)
r^3 = 12/27
r^3 = 4/9
r = (4/9)^(1/3)

To find the first term "a", we can substitute the value of "r" into the equation for the second term:
a*r = 20%9
a*(4/9)^(1/3) = 20%9
a = (20%9) / ((4/9)^(1/3))

To find the (n+1)th term, we can use the formula for the nth term of a geometric sequence:
a_n = a*r^(n-1)
a_(n+1) = a*r^n

So, the (n+1)th term is a*(4/9)^n.

Unfortunately, without knowing the value of "n", we cannot determine the exact value of the (n+1)th term.
1
×