Question

A geometric series has a common ratio of 3/5 series and an initial value of 1/2. Which of the following is not a term in the geometric series? 13/125 9/50 or 27/250​

Answer 1

Answer: 27/250​

Explanation:

Given :

b₁ = 1/2

q = 3/5

`\bullet ~~ \tt b _n = b_1 \cdot q^(n-1)`

Since we are looking for a term belonging to a given progression , then
n ∈ N , and this condition will be met only in the variant

`\displaystyle \large \boldsymbol{}b_n = (27)/(250) \\\\ b_1 \cdot q^(n-1) = (27)/(250) \\\\\\ (1)/(2) \cdot \bigg ((3)/(5) \bigg )^(n-1) = (27)/(250)\\\\\\ \bigg ((3)/(5) \bigg )^(n-1) = (27)/(125) \\\\\\ \bigg ((3)/(5) \bigg )^(n-1) = \bigg ((3)/(5) \bigg ) ^3\\\\\\ n -1 = 3 \\\\ n = 4 \in \mathbb N`