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

Question

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:

• $a_5=17$
• $a_n=5+(n-1)\cdot 3$
• $a_{50}=152$