Question

Indicate a general rule for the nth term of the sequence when a1 = √3 and r = 2.

Answer 1

The first term, a is √3 and the common ratio r is 2 and the general form of a geometric sequence is:

a(n)=a*r^(n-1) so:

a(n)=√3*2^(n-1)

Answer 2

`a_n = √(3) \cdot (2)^(n-1)`

Explanation:

The nth term for the geometric sequence is given by:

`a_n = a_1 \cdot r^(n-1)` ....[1]

where

`a_1` is the first term

r is the common ratio term.

As per the statement:

A sequence when
`a_1`= √3 and r = 2

then substitute these in [1] we have;

`a_n = √(3) \cdot (2)^(n-1)`

Therefore, a general rule for the nth term of the sequence is,
`a_n = √(3) \cdot (2)^(n-1)`