Insert 5 terms in arithmetic sequence between -8 and 22.

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lemjay | High School Teacher | (Level 3) Senior Educator

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If we are going to insert 5 terms between -8 and 22, the arithmetic sequence will be:

-8 , ___ , ___ , ___ , ___ , ___ , 22 

So, -8 is the first term and -22 is the seventh term.

To determine the common difference of arithmetic series, use the formula:

`a_n=a_1 + (n-1)d`

where `a_n`  the nth term                       `a_1` - the first term

            `n` - the number of terms            `d` - the common difference

Then, substitute `a_1=-8` and `a_7=22` and `n=7` to the formula.

`22 = -8 + (7-1)d`

`22=-8+6d`

`30=6d`

`5=d`

So the common difference is 5. Substitute this to the formula above to determine the 5 terms between -8 and 22.

`a_2=-8+(2-1)5 = -8+5=-3`

`a_3=-8+(3-1)5=-8+10=2`

`a_4=-8+(4-1)5=-8+15=7`

`a_5=-8+(5-1)5=-8+20=12`

`a_6=-8+(6-1)5=-8+25=17`

Hence, the arithmetic sequence is -8 , -3 , 2 , 7 , 12 , 17 , 22.

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