Q1915 Points Define a sequence a_0,a_1,a_2,\dotsa 0 ,a 1 ,a 2 ,… by a_0 = 3\text{ and } a_n = 3 + a_0 + a_1 + \dots + a_{n-1} \text{ for } n > 0.a 0 =3 and a n =3+a 0 +a 1 +⋯+a n−1 for n>0. Q19.11 Point Compute a_1a 1 , a_2a 2 , a_3a 3 , and a_4a 4 . Write down the values in the following blank parts. The first one is the value of a_1a 1 , the second one is the value of a_2a 2 , the third one is the value of a_3a 3 , and the last one is the value of a_4a 4 . You must only write down your final answer without any extra terms. For example, if your answer is 11, just write down 11 in the blank part. 6 12 24 48 Q19.25 Points Guess an explicit formula for a_na n . (This formula must give the exact value of a_na n .) You can either typeset your solution in the blank part or upload your solution to this problem. Choose FilesPlease select file(s)Select file(s) Q19.39 Points Use induction to prove that your formula in the previous part is correct. You can either typeset your solution in the blank part or upload your solution to this problem.

see explanation

step-by-step explanation:

since the sequence is geometric there is a common ratio r between consecutive terms, that is

r = 4 ÷ - 2 = - 2

r = - 8 ÷ 4 = - 2

r = 16 ÷ 8 = - 2

the next term - 13 must be incorrect as it should be - 32 for the sequence to be geometric.

the first 4 terms are therefore geometric with common ratio r = - 2

36

step-by-step explanation:

45

step-by-step explanation:

unless you made a typo, the answers are both a and c.

step-by-step explanation:

1.5/3 is .5 whereas 3/9 is .3333333 not proportional

22/33 is .66666 and 4/6 is also .66666 proportional

2/4 is .5 whereas 142/213 is .66666 not proportional

14/7 is 2 and 7/3.5 is also 2 proportional

you could've also checked it by doing this simple division:

if the larger fraction divides with the smaller fraction to equal 1, it is proportional. so let me show you what i mean:

when i divide 22/33 by 4/6 i get 1, so we know it is proportional, and it is the same with 14/7 and 7/3.5. now if i divide 3/9 by 1.5/3 i get .66666 so therefore we know it is not proportional.

there are many ways to do this so i wanted to show you some possible ways.