Question

Find the 11th term in this sequence. *10 poin1) -2, 4. -8, 16, ...Find a11

Answer 1

Given the terms

-2, 4, -8, 16

The first term = -2

The second term is 4

The third term is -8

The fourth term is 16

We can observe that this is a geometric sequence

So to get the 11th term, we will first get the formula

Step 1: Get the common ratio (r)

$\text{common ratio=}\frac{\sec ond\text{ term}}{first\text{ term}}=\frac{third\text{ term}}{\sec ond\text{ term}}$$r=\frac{4}{-2}=\frac{-8}{4}=-2$

Step 2: Get the formula for the nth term

The formula is given by

$T=r^n$

$T=(-2)^n$

where T is the nth term

n is the number of terms

Step 3: Find the 11th term

$T_{11}=(-2)^{11}$$T_{11}=-2048$

The 11th term is -2048