SOLUTION: Write a rule for the nth term of the sequence. Use your rule to find a100.–8, 9, 26, 43, 60, . . .

Algebra ->  Sequences-and-series -> SOLUTION: Write a rule for the nth term of the sequence. Use your rule to find a100.–8, 9, 26, 43, 60, . . .      Log On


   

Question 702642: Write a rule for the nth term of the sequence. Use your rule to find a100.–8, 9, 26, 43, 60, . . .
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
–8, 9, 26, 43, 60, . . .
a2 - a1 = 9-(-8) = 9+8 = 17
a3 - a2 = 26-9 = 17
a4 - a3 = 43-26 = 17
a5 - a4 = 60-43 = 17

So it is an arithmetic sequence with common
difference d = 17

an = a1 + (n-1)·d
an = -8 + (n-1)·17
an = -8 + 17(n-1)
an = -8 + 17n-17
an = -25 + 17n
an = 17n - 25

Checking:
a1 = 17(1) - 25 = 17 - 25 = -8
a2 = 17(2) - 25 = 34 - 25 =  9
a3 = 17(3) - 25 = 51 - 25 = 26
a4 = 17(4) - 25 = 68 - 25 = 43
a5 = 17(5) - 25 = 85 - 25 = 60
...
a100 = 17(100) - 25 = 1700 - 25 = 1675

Edwin