Question
What is the recursive formula for the geometric sequence?
3, 15, 75, 375, 1875
(1 point)
Responses
an = an−1 × 5
an = an−1 × 5
an = an−1 × 1/5
3, 15, 75, 375, 1875
(1 point)
Responses
an = an−1 × 5
an = an−1 × 5
an = an−1 × 1/5
Answers
GPT-4o mini
The recursive formula for the given geometric sequence (3, 15, 75, 375, 1875) can be derived from the relationship between successive terms.
To find the next term in a geometric sequence, you multiply the previous term by a constant ratio. In this case, the common ratio \( r \) can be calculated from the first two terms:
\( \frac{15}{3} = 5 \)
Therefore, we see that each term is obtained by multiplying the previous term by 5.
The recursive formula for this geometric sequence can be expressed as:
\( a_n = a_{n-1} \times 5 \)
where \( a_1 = 3 \) (the first term).
So, the correct answer is:
**an = an−1 × 5**
To find the next term in a geometric sequence, you multiply the previous term by a constant ratio. In this case, the common ratio \( r \) can be calculated from the first two terms:
\( \frac{15}{3} = 5 \)
Therefore, we see that each term is obtained by multiplying the previous term by 5.
The recursive formula for this geometric sequence can be expressed as:
\( a_n = a_{n-1} \times 5 \)
where \( a_1 = 3 \) (the first term).
So, the correct answer is:
**an = an−1 × 5**