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

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

## Answer: The 20th term of the sequence that begins −4, 8, −16, 32, ..... is 2097152.

Let's find the 20th term

**Explanation:**

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