Question

These are the first six terms of a sequence starting with a1=1.5: 1.5, – 6, 24, – 96, 384, – 15 These are the first six terms of a sequence starting with a1=1.5: 1.5, – 6, 24, – 96, 384, – 1536, ... Find an explicit formula for this sequence.36, ... Find an explicit formula for this sequence.

Answer 1

The explicit formula for the sequence is an = 1.5 * (-4)(n-1).

The given sequence is: 1.5, -6, 24, -96, 384, -1536, ...

To find an explicit formula for this sequence, we need to observe the pattern in the terms.

Notice that each term is obtained by multiplying the previous term by a factor of -4. This indicates a geometric sequence with a common ratio of -4.

Therefore, the explicit formula for this sequence is:

an = a1 * r(n-1)

Where a1 is the first term (1.5) and r is the common ratio (-4).