Question

given the sequence 5,8,11,14,17,20 explain what makes it arithmetic

It is arithmetic because you are ___ __ each time
state the fifth term of the sequence using subscript notation
a_5= ___

write an explicit formila ( (A_n=A_1+(n-1)D) for the given arithmetic sequence use your explicit formula to find the 50th term of the sequence
a_n=__+ (n-1) __
a_50=__+(__-1)__
a_50=___

Answer 1

The sequence 5, 8, 11, 14, 17, 20 is arithmetic because you are **adding 3** each time.

The fifth term of the sequence using subscript notation is \( a_5 = 17 \).

Now, let's write the explicit formula for the arithmetic sequence. The first term \( A_1 = 5 \) and the common difference \( D = 3 \). The explicit formula is:

\[
a_n = A_1 + (n-1)D = 5 + (n-1) \cdot 3
\]

To find the 50th term, we substitute \( n = 50 \) into the formula:

\[
a_{50} = 5 + (50 - 1) \cdot 3
\]
\[
a_{50} = 5 + 49 \cdot 3
\]
\[
a_{50} = 5 + 147
\]
\[
a_{50} = 152
\]

So, the answers are:
- \( a_5 = 17 \)
- \( a_n = 5 + (n-1) \cdot 3 \)
- \( a_{50} = 152 \)