Question

Find the first six terms of the sequence. a1 = -7, an = an-1 + 5

Answer 1

`-7,-2,\:3,\:8,\:13,\:18`

Explanation:

First Term

`a_1=-7`

Second Term

`a_n=a_(n-1)+5\\\\a_2=a_(2-1)+5\\\\a_2=a_1+5\\\\a_2=-7+5\\\\a_2=-2`

Third Term

`a_3=a_(3-1)+5\\\\a_3=a_2+5\\\\a_3=-2+5\\\\a_3=3`

Fourth Term

`a_4=a_(4-1)+5\\\\a_4=a_3+5\\\\a_4=3+5\\\\a_4=8`

Fifth Term

`a_5=a_(5-1)+5\\\\a_5=a_4+5\\\\a_5=8+5\\\\a_5=13`

Sixth Term

`a_6=a_(6-1)+5\\\\a_6=a_5+5\\\\a_6=13+5\\\\a_6=18`

All you are doing is just adding 5 to -7 to get the next term each time for 6 times!