Question

Indicate the general rule for the arithmetic sequence with a3 = -4 and a8 = -29. an = -6 + (n-1)(-5) an = -6 + (n-1)(5) an = 6 + (n-1)(-5) an = 6 + (n-1)(5)

Answer 1

The explicit formula for an arithmetic series is given by:
an=a+(n-1)d
given that:
a3=-4 and a8=-29
then we can formulate the equations given by:
-4=a+(3-1)d
-4=a+2d.....i

and
-29=a+(8-1)d
-29=a+7d.....ii
i and ii are simultaneous equations, thus we shall solve them as follows:
subtract i from ii we get:
-25=5d
thus
d=-5
substituting d=-5 in i and solving for a gives us:
-4=a+2(-5)
-4=a-10
⇒a=6
thus the explicit formula for our series will be:
an=6-5(n-1)