Question

Find the 75th term of the arithmetic sequence -17, -13, -9, ...−17,−13,−9,...

Answer 1

The terms in this sequence are 4 units apart. If
`a_1=-17` is the first term in the sequence, then the next few terms are obtained by adding 4 to the preceding term:

`a_2=a_1+4=-13`

`a_3=a_2+4=a_1+2\cdot4=-9`

`a_4=a_3+4=a_1+3\cdot4=-5`

and so on, leading up to the
`n`th term

`a_n=a_(n-1)+4=a_(n-2)+2\cdot4=\cdots=a_1+(n-1)\cdot4`

`\implies a_n=-17+4(n-1)=4n-21`

Then the 75th term in the sequence is

`a_(75)=4\cdot75-21=279`