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 = -200
a₃ = 400
a₄ = \square

Explanation:

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

The formula for the \(n\)th term of a geometric sequence is \(a_{n}=a_{1}\times r^{n - 1}\). Another way to find subsequent terms is \(a_{n}=a_{n-1}\times r\).

Step2: Find \(a_{4}\) using the relation \(a_{n}=a_{n - 1}\times r\)

We know that \(a_{3}=400\) and \(r=-2\).
Using the formula \(a_{n}=a_{n-1}\times r\), for \(n = 4\), we substitute \(a_{3}\) and \(r\) values.
\(a_{4}=a_{3}\times r\)
\(a_{4}=400\times(-2)\)

Answer:

\(-800\)