Hello! I could use some help with these questions on sequences and series for functions so that I can cross-reference with my work

Question

a) Find S₉ of a geometric series if t₁ = 2 and t₆ = 486.

b) What binomial power does the binomial expansion  represent? Indicate the binomial base as well as the exponent. Explain how you figured out your answer.

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

d) The 3rd term of a geometric sequence is 36, and the 6th term is . What is the recursive formula for the sequence?

Answer 1

t1=2

t6=486

tn = 2(r^n-1)

t6 = 2(r^5) = 486

r^5 = 486/2 = 243

r = 5th root of 243=3

s9 = a1(r^n-1)/(r-1)= 2(3^9-1/(3-1)= 13,121

d) geometric sequence

a3 = 36

a6 = 9/2

a4 = 18

a5 = 9

a6 = 9/2

common ratio = r = 1/2

an = .5an-1, each term is 1/2 the preceding term

a3 =36

a2 =72

a1 = 144

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

a3 = 144(.5^2) = 144(1/4 = 36

a6= 144((1/2)^5) = 144/2^5 = 144/32= 4.5= 9/2