140k views
3 votes
Find the first four terms and state terms given the geometric sequence with a as the first term.

An=4.7•-6.0^n-1,a6


An=5^n-1,a7


An=2.1•5.0^n-1,a6


An=2n,a6




Someone please help me and show me how to do it

1 Answer

5 votes

The first four terms of the sequence are; An=4.7•-6.0ⁿ⁻¹ = (1, -1.3, 1.69, 1.69, and −2.197)

An=5ⁿ⁻¹ = (1, 5, 25, and 125)

An=2.1•5.0ⁿ⁻¹ = (10.5, 10.5, 52.5, 262.5)

An=2n (2, 4, 6, 8)

How to obtain the terms in a geometric sequence

If you have the explicit formula for the geometric sequence, like An = a * r^(n-1), where:

a is the first term

r is the common ratio

n is the term number,

you can simply substitute the desired term number (n) into the formula and calculate the corresponding value.

So, for the first sequence, we would have;

4.7 * -6.0 = -1.3ⁿ⁻¹

1 = -1.3¹⁻¹

= -1.3⁰

= 1

The second term would be -1.3ⁿ⁻¹

-1.3²⁻¹

= -1.3¹

= -1.3

The third term would be -1.3³⁻¹

= -1.3²

=1.69

The fourth term would be -1.3⁴⁻¹

= -1.3³

= -2.197

User Davy Meers
by
8.5k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.