# What is the 20th term of the sequence that begins -4, 8, -16, 32, ..... ?

**Solution:**

If the ratio between two consecutive terms in a sequence is same throughout, then the sequence is called a geometric progression.

Given Sequence: -4, 8, -16, 32,.....

To find the n^{th} term we will apply the formula a_{n }= ar^{n-1 }where,

First term (a) = -4

2^{nd} term / 1^{st} term = 8 / (-4) = -2

3^{rd} term / 2^{nd} term = -16 / 8 = -2

Thus, Common Ratio (r) = -2

n = 20

⇒ a_{n }= ar^{n - 1 }

⇒ a_{20 }= - 4 × (-2)^{20 - 1 }

⇒ a_{20 }= - 4 × (-2)^{19}

⇒ a_{20 }= - 4 × (-524288)^{ }

⇒ a_{20 }= 2097152

Thus, the 20th term of the sequence is 2097152.

## What is the 20th term of the sequence that begins -4, 8, -16, 32, ..... ?

**Summary:**

The 20th term of the sequence that begins -4, 8, -16, 32, ..... is 2097152.

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