Question

Write explicit formula for a1=3, r=-2; then generate 1st 5 terms

Answer 1

Answer:

• an = 3(-2)^(n-1)
• 3, -6, 12, -24, 48

Step-by-step explanation:

These variable names, a1, r, are commonly used in relationship to geometric sequences. We assume you want the terms of a geometric sequence with these characteristics.

a1 is the first term. r is the ratio between terms, so is the factor to find the next term from the previous one.

  a1 = 3  (given)

  a2 = a1×r = 3×(-2) = -6

  a3 = a2×r = (-6)(-2) = 12

  a4 = a3×r = (12)(-2) = -24

  a5 = a4×r = (-24)(-2) = 48

The first 5 terms are 3, -6, 12, -24, 48.

__

The explicit formula for the terms of a geometric sequence is ...

  an = a1×r^(n -1)

Using the given values of a1 and r, the explicit formula for this sequence is ...

  an = 3(-2)^(n -1)