Consider the infinite geometric series: Σ∞ k=1 1/6(-1/10)^k-1

What is a1?

What is r?

Find the following partial sums:

S2 = 3/20 101/660 11/60

S3 = 3/20 91/600 101/540

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1) 2/5

2) zero=0/1

3) zero=0/2

4) -4/5

5) undefined=3/0

(a) common ratio in the given sequence is, 3

(b) push ups will do kendall do on the 20th week

step-by-step explanation:

geometric sequence is a sequence of numbers that follows a pattern were the next term is found by multiplying by a constant called the common ratio(r)

(a)

given the sequence: 6 , 18 , 54 , 162 ,

this sequence is geometric sequence where each term is 3 times the previous term.

therefore,

common ratio(r) = 3.

(b)

a formula for nth term of geometric sequence is given by;

,   where r is the common ratio between the successive terms and is the first term,

to find how many push ups will kendall do on the 20th week.

here. n = 20th term.

in the given sequence first term

then;

simplify:

therefore, push ups will do kendall do on the 20th week