terms Of algebra

Question

9. The first 9 terms of 12, – 6 ,+ 3, - …

10. The first 15 terms of -1, + 1, -…

11. The first 6 terms of 1, + 3, + …

12. The first 10 terms of 2, – 4, 

Answer 1

12, -6, 3, -3/2, 3/4, -3/8, 3/16, -3/32, 3/64,...

it's a geometric sequence, with a common ratio, r=-1/2

each term is -1/2 times the preceding term

an=a1(r)^(n-1) =12(-1/2)^(n-1)

a9 = 12(-1/2)^(8) =12(1/256)= 3/64

-1,+1,-1,+1,-1,+1,-1,+1,-1,+1,-1,+1,-1,+1,-1,...

another geometric sequence with common ratio = -1

a15=-1(-1)^14=-1(1)=-1

It might have been an arithmetic sequence with common difference of 2, but -1,+1,- ...has the negative sign for the 3rd term, so that rules out an arithmetic sequence

1,3,5,7,9,11,...

an arithmetic sequence with common difference,d=2

an=a1 +(n-1)d

a6= 1+(6-1)(2) =11

or it might be a geometric sequence with common ratio,r=3

1,3,9,27,81,243,...

an=a1(r)^(n-1)

a6 =1(3)^5 =3^5 = 243

2,-4,8,-16,32,-64, 128, -256,512,-1024 ...

as a geometric sequence with common ratio, r=-2

an=2(-2)^(n-1)

a10=2(-2)^(9) =2(-512) =-1024

or 2,-4,...

might also be an arithmetic sequence with common difference, d=-6

an=a1+(n-1)(d)

a10=2 +(9)(-6)= 2-54=-52

2,-4,-10,-16,-22,-28,-34,-40,-46,-52,...