Question

PLEASE HELP!!!!!

Answer 1

We have that

   Part 1.] Match the following items.   
1. 2, 4, 8, 16, . . ., 64---------- > B. finite sequence
2. 3, 6, 9, 12, . . . ------------- > C. infinite sequence
3. 3 + 9 + 27 + 81 + . . .------> D. geometric series
4. 3 + 5 + 7 + 9 + . . .----------> A. arithmetic series
5. 3, -3, 3, -3, 3,-3, . . .-------- >E. alternating sequence

  Part 2.]-3, 6, -9, 12, -15, . . .
Which of the following represents the general term for the sequence given?
A. (-1^n)*(3^n)
for n=1-----------> (-1^1)*(3^1)=-3
for n=2-----------> (-1^2)*(3^2)=9 -------------- a2=6 no represents

B. (-1^n)*(3n)
for n=1-----------> (-1^1)*(3*1)=-3
for n=2-----------> (-1^2)*(3*2)=6
for n=3-----------> (-1^3)*(3*3)=-9
for n=4-----------> (-1^4)*(3*4)=12
for n=5-----------> (-1^5)*(3*5)=-15

C. (-1^(n+1))*(3)
for n=1-----------> (-1^(1+1))*(3)=3---------- > a1=-3 no represents

the answer part B is option B. (-1^n)*(3n)

Part 3.] The first attached picture

Σ (2n+1)  for n=1 to 5
n1---------> (2*1+1)=3
n2---------> (2*2+1)=5
n3---------> (2*3+1)=7
n4---------> (2*4+1)=9
n5---------> (2*5+1)=11
Σ (2n+1)  for n=1 to 5=[3+5+7+9+11]=35

the answer part C is 35

Part 4.] The second attached picture

Σ (3n)  for n=1 to 3
n1---------> (3*1)=3
n2---------> (3*2)=6
n3---------> (3*3)=9
Σ (3n)  for n=1 to 3=[3+6+9]=18

the answer part 4 is 18

Part 5.] The third attached picture
Σ (2n+2)  for n=1 to 4
n1---------> (2*1+2)=4
n2---------> (2*2+2)=6
n3---------> (2*3+2)=8
n4---------> (2*4+2)=10
Σ (2n+2)  for n=1 to 4=[4+6+8+10]=28

the answer part 5 is 28

Part 6.] Which of the following best describes the following set of numbers?
6+8+10+12+...+(4+2n)+...
8-6=2
10-8=2
12-10=2
the next number is obtained by adding 2 to the previous number
this is an  Arithmetic Series

the answer is the option D. Arithmetic Series