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Write the equation for the nth term of each geometric sequence.

1,1,1,1,.....

Short Answer

Expert verified

The nth term of the series 3,9,27,.....is an=(1)n.

Step by step solution

01

Step 1. State the concept used.

In mathematics, a geometric progression, also known as a geometric sequence, is a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.

For example, the sequence 2,6,18,54,...is a geometric progression with common ratio 3.

The ration of 2ndterm and first term is called the common ratio.

02

Step 2. Find the common ratio.

The sequence:1,1,1,1,.....

Each term in a geometric sequence can be expressed in terms of the first terma1 and the common ratio r. Since each succeeding term is formulated from one or more previous terms, this is a recursive formula.

First-terma1=1and the common ratio is:

r=  a2a1=1(1)=1

03

Step 3. Find the nth term.

In order to calculate the nth term substitute -1for a1into the formulaan=a1rn1.

an=1×(1)n1=(1)1×(1)n1=(1)1+n1=(1)n

The nthterm of the series 1,1,1,1,.....isan=(1)n.

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