Question

Find the missing terms of the arithmetic sequence.​ (Hint: The arithmetic mean of the first and fifth terms is the third​ term.)

3​, a 2​, a 3​, a 4​, negative 13​, ...

Answer 1

The arithmetic sequence is: 3, -1, -5, -9, -13

Explanation:

Recall that the nth term of an arithmetic sequence is defined via the formula:

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

where d is the common difference, n is the term number, and
`a_1` is the first term.

Since we know what the first and fifth terms are (3 and -13 respectively), we can find the common difference and with it any of the missing terms:

`a_n=a_1+(n-1)*d\\a_5=a_1+(5-1)*d\\-13=3+(4)*d\\-16=4*d\\d=-(16)/(4) \\d=-4`

now that we know d=-4, we can find the missing terms:

`a_2=3+(2-1)*(-4) = -1\\a_3=3+(3-1)*(-4)= -5\\a_4=3+(4-1)*(-4)=-9`