Question

Find the first 5 terms of the arithmetic sequence : a(1)=-3 , a(17)=-20

Answer 1

The explicit formula for arithmetic sequence is:
an=a+(n-1)d
where:
a=first term
d=common difference 
given:
a3=22
a(17)=-20
substituting this in our equation we get:
22=a+(3-1)d
22=a+2d
a=22-2d........i

also:
-20=a+(17-1)d
-20=a+16d.....ii
but substituting i in ii we get:
-20=22-2d+16d
-20-22=14d
-42=14d
d=-3
but:
a=22-2d
a=22-2(-3)
a=28
thus the formula will be:
an=28-3(n-1)
thus the first term will be 28
the 2nd term will be:
a2=28-3(2-1)
a2=25

the 3rd term will be:
a3=28-3(3-1)
a3=28-6
a3=22

a4=28-3(4-1)
a4=28-9
a4=15

a5=28-3(5-1)
a5=28-3(4)
a5=28-12
a5=15