Question

In an infinite geometric sequence, the first term is 3, and the common ratio is 0.5. What is the value of the 4th term?

a) 0.375
b) 1.5
c) 0.75
d) 3

Answer 1

In an infinite geometric sequence with a first term of 3 and a common ratio of 0.5, the value of the 4th term is calculated using the formula for the nth term and is found to be 0.375.

Step-by-step explanation:

The question is asking for the value of the 4th term in an infinite geometric sequence with the first term being 3 and a common ratio of 0.5.

To find the 4th term, we apply the formula for the nth term of a geometric sequence, which is an = a1 × r(n-1), where an is the nth term, a1 is the first term, r is the common ratio, and n is the term number.

Substituting our values, we get the 4th term as follows: a4 = 3 × (0.5)(4-1) = 3 × (0.5)3 = 3 × 0.125 = 0.375.

Therefore, the value of the 4th term is 0.375, which corresponds to option a.