Help with arithmetic sequences?

Question

FIND THE MISSING TEMS IN EACH ARITHMETIC SEQUENCE

5,_,_,_,-3

Answer 1

If the sequemce is arithmetic then it must be:

5,3,1,-1,-3

an arithmetic sequence is a sequence of terms a_n, where a_n=s+bn, where b is the "start term". So you have

s+b=5,   (the first term where n=1) and

s+5 b =-3 (the fifth term)

subtracting the 1st equ. from the 2nd gives,

4b =-8 and

b=-2

Substituting b=-2 into the 1st equation gives s=7

So the general equation of your arithmetic progression is

a_n=7-2n   (a_n means "a sub n" or the nth term)

So substituting n=2,3,and4 into a_n=7-2n    gives your answer.

Cheers.