Question

Indicate a general rule for the nth term of the sequence when a1 = 5 and r = √3 .

Answer 1

`a_n = 5*(√(3)) ^(n-1)`

Explanation:

The n-th term of a geometric sequence
`a_n = a_1r^(n-1)`, where
`a_n` is the n-th term,
`a_1` is the first term, n is the number of terms.

Given:

`a_1 = 5 ; r = √(3)`

Now plug in the given values in the n-th term formula, we get

Therefore, the general rule for n-th term of the sequence is
`a_n = 5*√(3) ^(n-1)`

Answer 2

For a geometric sequence with first term a_1 = 5 and common ratio r = sqrt(3), the general formula for the nth term is:
a_n = (a_1)(r)^(n - 1)
In this case,
a_n = 5(sqrt3)^(n - 1)