Question

Vera and Fenyang were asked to find an explicit formula for the sequence 26, 10, -6, -22,... where the first term should be g(1). What is the explicit formula for this sequence?

a) g(n) = 26 - 16n
b) g(n) = 26 - 8n
c) g(n) = 26 - 12n
d) g(n) = 26 - 4n

Answer 1

The explicit formula for the sequence is g(n) = 26 - 16n, making the correct choice a) from the provided options.

Step-by-step explanation:

The question requires us to find an explicit formula for a sequence with terms 26, 10, -6, -22,... where the first term is represented by g(1).

To find the pattern, we calculate the differences between the terms:

• 10 - 26 = -16
• -6 - 10 = -16
• -22 - (-6) = -16

Noticing that the common difference is -16, we can determine that this is an arithmetic sequence.

We can write the explicit formula as g(n) = first term + (n - 1) * common difference. Substituting the first term, g(1) = 26, and the common difference, -16, into the formula, we get: g(n) = 26 + (n - 1)(-16) = 26 - 16n + 16

Therefore, simplifying the formula, we find that the explicit formula is: g(n) = 26 - 16(n - 1)

The correct choice is: a) g(n) = 26 - 16n.