Question

What is the 7th term in the geometric sequence described by this explicit formula?an = –3 • (3)(n – 1)

Answer 1

7th term is -2187

Explanation:

Nth term of the geometric sequence is given by

`a_n = a_1(r)^(n-1)`

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

`a_n = -3(3)^(n-1)`

a1=-3 and r=3

7 th term of the geometric sequence is

`a_7 = a_1(r)^(6)`

replace the values of a1 and 'r'

`a_7 = -3(3)^(6)`

a_7=-2187

Answer 2

7th term = -2187

Explanation:

The formula for nth term of a geometric sequence is given by:

`a_n=a*r^(n-1)`

Where

• a is the first term,
• r is the common ratio,
• n is the nth term (term number)

Since the question gives us the formula and wants to know 7th term, we just plug in 7 into n:

`a_n=(-3)*(3)^(n-1)\\a_n=(-3)*(3)^(7-1)\\a_n=(-3)*(3)^6\\a_n=-2187`