Question

Create a formula to find a_(n) for the sequence 3,-6,12,-24??

Answer 1

The formula to find the nth term, a_n, for the sequence 3, -6, 12, -24 is a_n = 3 × (-2)^(n-1), where 3 is the first term and -2 is the common ratio.

Step-by-step explanation:

To create a formula for the nth term, a_n, for the sequence 3, -6, 12, -24, we need to find a pattern in the sequence. First, we notice that each term is the previous term multiplied by -2. Therefore, the sequence is a geometric sequence with a common ratio of -2. To find the formula for the n-th term of a geometric sequence, we use the formula:

a_n = a_1 × r^(n-1),

where a_1 is the first term and r is the common ratio. For our sequence:

• a_1 = 3
• r = -2

So the formula to find the n-th term, a_n, is:

a_n = 3 × (-2)^(n-1)