Question

Find a formula for the general term a n of the sequence assuming the pattern of the first few terms continues. { − 13/3 , 16/9 , − 19/27 , 22/81 , − 25/243 , ... }

Answer 1

a formula for the general term a n of the sequence assuming the pattern of the first few terms continues. { − 13/3 , 16/9 , − 19/27 , 22/81 , − 25/243 , ... } is $(-1)^n\frac{13+3(n-1)}{3^n}$ .

Step-by-step explanation:

Here we have , the pattern of the first few terms continues. { − 13/3 , 16/9 , − 19/27 , 22/81 , − 25/243 , ... } . We need to find a formula for the general term a n of the sequence . Let's find out:

In this question there is no such technique , instead we have to use our brain to manipulate the pattern as :

1st term = − 13/3 = $(-1)^1\frac{13 }{3^{1}}$

2nd term = 16/9 = $(-1)^2\frac{13+3(1)}{3^2}$

3rd term = − 19/27 = $(-1)^3\frac{13+3(2)}{3^3}$

4th term = 22/81 = $(-1)^4\frac{13+3(3)}{3^4}$

5th term = − 25/243 = $(-1)^5\frac{13+3(4)}{3^5}$

nth term = $(-1)^n\frac{13+3(n-1)}{3^n}$

Therefore, a formula for the general term a n of the sequence assuming the pattern of the first few terms continues. { − 13/3 , 16/9 , − 19/27 , 22/81 , − 25/243 , ... } is $(-1)^n\frac{13+3(n-1)}{3^n}$ .