Question 702642
–8, 9, 26, 43, 60, . . .
<pre>
a<sub>2</sub> - a<sub>1</sub> = 9-(-8) = 9+8 = 17
a<sub>3</sub> - a<sub>2</sub> = 26-9 = 17
a<sub>4</sub> - a<sub>3</sub> = 43-26 = 17
a<sub>5</sub> - a<sub>4</sub> = 60-43 = 17

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

a<sub>n</sub> = a<sub>1</sub> + (n-1)·d
a<sub>n</sub> = -8 + (n-1)·17
a<sub>n</sub> = -8 + 17(n-1)
a<sub>n</sub> = -8 + 17n-17
a<sub>n</sub> = -25 + 17n
a<sub>n</sub> = 17n - 25

Checking:
a<sub>1</sub> = 17(1) - 25 = 17 - 25 = -8
a<sub>2</sub> = 17(2) - 25 = 34 - 25 =  9
a<sub>3</sub> = 17(3) - 25 = 51 - 25 = 26
a<sub>4</sub> = 17(4) - 25 = 68 - 25 = 43
a<sub>5</sub> = 17(5) - 25 = 85 - 25 = 60
...
a<sub>100</sub> = 17(100) - 25 = 1700 - 25 = 1675

Edwin</pre>