Sequences and series questions

Question

a) The sum of a geometric sequence 2 – 6 + 18 – 54 + ... –  is –29 524. Find the number of terms.

b) Find S₁₇ for the series 8 – 4 + 2 – 1+ ...

Answer 1

r=-3

sn=a1(r^n -1)/(r-1)

-29524=2((-3)^n-1)/(-3-1)

59048= (-3)^n -1

59049= (-3)^n n is an even integer

3^n = 59049

n= 10

10 terms

8,-4,2,-1,1/2,-1/4,1/8,-1/16,1/32,-1/64,1/128,, -1/256,

1/512, -1/1024, 1/2048, -1/4096, 1/8192=17th term

odd terms are >0

an=a1(r^(n-1)

a17=8(-.5^16)=8/2^16=8/65536=1/8192