Question

For the following geometric sequence find the explicit formula {1,-3,9,...}

Answer 1

Answer:

$a_n=1\cdot (-3)^{(n-1)}$

Step-by-step explanation:

We have been given a geometric sequence and we are asked to find the explicit formula for our given sequence.

The explicit formula of geometric sequence is in form: $a_n=a_1\cdot r^{(n-1)}$, where,

$a_n=\text{nth term of sequence}$,

$a_1=\text{1st term of sequence}$,

$r=\text{Common ratio}$,

$n=\text{Number of term}$.

First of all, let us find common ratio of our given sequence by dividing one term by its previous term.

$r=\frac{-3}{1}=-3$

We can see that 1st term of our given sequence is 1. Upon substituting our given values in explicit form of geometric sequence we will get,

$a_n=1\cdot (-3)^{(n-1)}$

Therefore, the explicit formula for our given sequence is $a_n=1\cdot (-3)^{(n-1)}$.

Answer 2

The first term of this series (a+1) is 1 and the common ratio (r) is -3.

Thus, the explicit formula is a_n = 1*(-3)^(n-1).

Must check this!  suppose we try to calculate the 3rd term.  Then n = 3.

a_3 = 1*(-3)^(3-1) = (-3)^2 = 9.  This is correct.