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Anna11 [10]
3 years ago
5

What is the 6th term of the geometric sequence 4, −20, 100, ...?

Mathematics
2 answers:
shtirl [24]3 years ago
3 0
Let's calculate r of this G.P: (-20)/(4) = - 5(100)/(-20) = - 5So r = -5
The formula to find the nth term of a GP is;
a(n) = a(r)ⁿ⁻¹
<u />a₆ = a(r)⁶⁻¹
a₆ = 4(-5)⁵ = -12500<u />
Umnica [9.8K]3 years ago
3 0

Answer:

the 6th term of the given sequence is, - 12500

Step-by-step explanation:

The nth term for the geometric sequence is given by:

a_n = a_1 \cdot r^{n-1}      ....[1]

where,

a_1 is the first term

r is the common ratio of the terms.

Given the sequence:

4, −20, 100, ...

This is a geometric sequence.

Here,

a_1 =4 and r = -5

We have to find the 6th term of the given sequence:

Substitute n= 6 and the given values in [1] we have;

a_6 = 4 \cdot (-5)^5 = 4 \cdot -3125 = -12500

therefore, the 6th term of the given sequence is, - 12500

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