Given the first term and the common ratio of a geometric sequence, write the formula and find the 6th term. A1=-4 and r=3

Answer 1

The formula is An = A1 * r^(n-1),

since n starts with 1, so in our case

An = -4 * 3^(n-1). Therefore, the 6th term = A6 = -4 * 3^(6-1) = -4 * 3^5 = -4 * 243 = -972.

Answer 2

The explicit form for a geometric sequence, which is in your text book, is:

a_n = a₁·r^n-1

where a_n is the nth term in the sequence, a₁ is the first term in the sequence, and r is the common ratio, The problem tells you what a₁ and r are, so fill them into the formula to "write the formula". To find the value of the 6th term, set n = 6 and compute the answer.