Final answer:
The formula for the given geometric sequence 5, -15, 45, -135, 405 is an = a1 * rn-1, where a1 = 5, r = -3, and n represents the position of the term in the sequence.
Step-by-step explanation:
The given sequence is: 5, -15, 45, -135, 405.
A geometric sequence is a sequence in which each term is found by multiplying the previous term by a constant value called the common ratio. Let's find the common ratio for this sequence.
Divide each term by its previous term: -15 ÷ 5 = -3, 45 ÷ -15 = -3, -135 ÷ 45 = -3, 405 ÷ -135 = -3.
The common ratio, in this case, is -3. Therefore, the formula for the given geometric sequence is:
an = a1 * rn-1
where:
- an represents the 'n'th term of the sequence.
- a1 represents the first term of the sequence, which is 5.
- r represents the common ratio, which is -3.
- n represents the position of the term in the sequence.