Question

How many terms are in the sequence? Please show all work

Answer 1

We need to find how many terms are in the given sequence:

Which starts with 3,7,11 until 123.

Now, looking at the sequence, it has a common difference:

7-3 = 4

11-7= 4

So, the common difference is 4.

Then,

3,7,11,11+4=15, 15+4= 19,19+4= 23 ............. 123

So, if the sequence goes on,we use the next formula:

`T_n=a+\left(n+1\right)d`

Where d=common difference

Tn = the n term

n= total terms

Replacing:

`\begin{gathered} 123=3+\left(n-1\right)4 \\ Solve\text{ for n} \\ 123-3=\left(n-1\right)4 \\ 120=4n-4 \\ 120+4=4n \\ Then \\ n=(124)/(4) \end{gathered}`

Therefore, the total number for the sequence is 31