Evaluate the sequence

Question

For the sequence A_n=2+5*(n-1),

the first term is?

the second term is?

the third term is?

the fourth term is?

the fifth term is?

the common difference (d) is?

 

Answer 1

Hi Dalia:

 

A_n = 2 + 5*(n-1), where n= 1, 2, 3, ...

 

The first term occurs when n=1:

 

A₁ = 2 + 5(1-1) = 2

 

The other terms work the same way, just plug in the different values of n (n = 2, 3, 4, 5).

 

The common difference is just the difference between one term and the next one after it.  To compute it, do the following subtraction:

 

Common Difference = A_n+1 - A_n

 

where

 

A_n+1 = 2 + 5((n+1) - 1) = 5n + 2

A_n = 2 + 5(n-1) = 2 + 5n - 5 = 5n - 3

 

Subtract A_n from A_n+1 to get the answer.  Let me know what you get in the comments and I'll let you if it's right.