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= -800 a₅=□

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 \(a_{n}=a_{1}r^{n - 1}\). For \(n = 5\), we can also use the relation \(a_{n}=a_{n-1}\times r\). Since we know \(a_{4}=-800\) and \(r=-2\).

Step2: Calculate \(a_{5}\)

Using the relation \(a_{n}=a_{n - 1}\times r\), substitute \(n = 5\), \(a_{4}=-800\) and \(r=-2\). Then \(a_{5}=a_{4}\times r\).

$$a_{5}=(-800)\times(-2)$$

$$a_{5}=1600$$

Answer:

\(1600\)