Find the 10th term of the geometric sequence 10, -20, 40, ...

-5120

Step-by-step explanation:

a = 10

r = -2

Tenth term: 10(-2)⁹

= -5120

the 10th term is - 5120

Step-by-step explanation:

In a geometric sequence, consecutive terms differ by a common ratio.

The formula for determining the nth term of a geometric progression is expressed as

an = a1r^(n - 1)

Where

a1 represents the first term of the sequence.

r represents the common ratio.

n represents the number of terms.

From the information given,

a1 = 10

r = - 20/10 = 40/ - 20 = - 2

n = 10

The 10th term, T10 is

T10 = 10 × - 2^(10 - 1)

T10 = 10 × - 2^9

T10 = 10 × - 512

T10 = - 5120