Question

Find the 21st term of the geometric sequence that begins 2,6,18,54,...

Answer 1

Answer:

6973568802

Step-by-step explanation:

I memorized the equation: A(n) = A(1)*d^(n-1).

You can plug into the equation A(21) = 2*3^20, which can be solved to 6973568802. (I solved this step through a calculator by finding 3^20, then multiplying that by 2 to get 6973568802.

Hope this helps!

Answer 2

Answer:

21st term is 6973568802

Step-by-step explanation:

2,6,18,54,...

nth term of  geometric sequence is

$a_n= a_1(r)^{n-1}$

Where a1 is the first term and 'r' is the common ratio

a1= 2

To find common ratio , divide the second term by first term

$\frac{6}{2} =3$

$\frac{18}{6} =3$

a1=2 and r= 3

$a_n= a_1(r)^{n-1}$

$a_n= 2(3)^{n-1}$

To find 21 term , replace n with 21

$a_{21}= 2(3)^{21-1}$

$a_{21}= 2(3)^{21-1}$

21st term is 6973568802