Question

Write the explicit formula given the first term and the common ratio for a geometric sequence.

G1 = 3, r = 10

Answer 1

An explicit formula for a geometric sequence with a first term of 3 and a common ratio of 10 is Gn = 3 × 10n-1. This allows calculation of any term in the sequence.

Step-by-step explanation:

The subject of this question is Mathematics and it pertains to geometric sequences, specifically required to find an explicit formula for a geometric sequence. Given the first term (G1) of 3 and a common ratio (r) of 10, the explicit formula for the nth term of a geometric sequence is Gn = G1 × rn-1.

Using the provided values, the formula becomes Gn = 3 × 10n-1. This means that to find the nth term of this sequence, you multiply the first term, 3, by 10 raised to the (n - 1) power.