Question

write the first six terms of of the geometric sequence with the first term, a₁, and common ratio, r. a₁ = 100, r = -2 a₂ = \square

Explanation:

Step1: Use the formula for the \(n\)th term of a geometric sequence

The formula for the \(n\)th term of a geometric sequence is \(a_{n}=a_{1}\times r^{n - 1}\). For \(n = 2\), we have \(a_{2}=a_{1}\times r^{2 - 1}=a_{1}\times r\).

Step2: Substitute the given values of \(a_{1}\) and \(r\)

Given \(a_{1}=100\) and \(r=- 2\). Then \(a_{2}=100\times(-2)\).

$$a_{2}=100\times(-2)=-200$$

Answer:

\(-200\)