Question

5.

Geometric Sequence goes from one term to the next by always multiplying by the same
value.
Examples:
1, 2, 4, 8, 16,...... common multiplier is multiply by 2
27, 9, 3, 1, 2,........ Common multiplier is multiplied by 13
t(n) = ab"
b= common multiplier
n = term # (the nth term)
a= zeroth term
Given the sequence 70, 49, 34.3, 24.01, ....
a. What is the common multiplier?
b. What is the zeroth term?
c. What is the value of the 25th term t(25)?

Answer 1

Answer: See explanation

Explanation:

a. What is the common multiplier?

This will be gotten by dividing the second term by the first term. This will be:

= 49/70 = 0.7

Common multiplier = 7/10 or 0.7

b. What is the zeroth term?.

a = 70

The zeroth term is 70

c. What is the value of the 25th term t(25)?

nth term = ar^n-1

25th term = ar^25-1

= ar^24

= 70 × 0.7^24

= 70 × 0.0001916

= 0.013412