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} 

⇒ a₂₀ = - 4 × (-2)^{20 - 1} 

⇒ a₂₀ = - 4 × (-2)¹⁹

⇒ a₂₀ = - 4 × (-524288) 

⇒ a₂₀ = 2097152

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

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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.