Given the geometric sequence, find an explicit formula

Question

Given the geometric sequence: 14, (140/11), (1400/121)....

Find an explicit formula for A_n.

A_n=

Find A₁₁=

 

 

Answer 1

Geometric sequence is a sequence where a term is found by multiplying the previous term by a number (common ratio).

 

A_n = A₁ * (k)ⁿ    k is the common ratio, and A₁ is the first term

 

You have to find the common ratio, and then you can write the equation.

If you are confused about how to find the common ratio, try do the previous problem first.

 

After you write the equation for A_n you can find A₁₁ by replacing n with 11. Use your calculator.

Answer 2

An= (14*10^n-1)/(11^n-1) so that A11=(14* 10^10)/(11^10)

Answer 3

Here's a little clue to help you get on track:

 

This sequence is 14(10^0/11^0), 14(10^1/11^1), 14(10^2/11^2), 14(10^3/11^3),...

 

So, the terms are:

1. 14(1/1) or 14

2. 14(10/11) or 140/11

3. 14(100/121) or 1400/121

4. 14(1000/1331) or 14000/1331

etc.

 

Express the exponents as terms in the sequence:

The 1st term gets an exponent of zero;

The 2nd term gets an exponent of one;

The 3rd term gets an exponent of two;

etc.

 

So each term gets an exponent of n-1. Good luck!

Answer 4

A(n)=14(10/11)^n for n=0,1,2,3,4,...

n=0, A(0)=14

n=1, A(1)=140/11

n=2, A(2)=14(100/121)=1400/121

n=3, A(3)=14(1000/1331)=14,000/1331

.

.

n=11, A(11)=14(10/11)^11=14(10^11)/(11^11)=14(100,000,000,000)/285,311,670,611=

1,400,000,000,000/285,311,670,611