PLEASE HELP7.05a1. Find the first six terms of the sequence.a1 = -6, an = 4 • an-1 A) 0, 4, -24, -20, -16, -12 B) -24, -96, -384, -1536, -6144, -24,576 C) -6, -24, -20, -16, -12, -8 D) -6, -24, -96, -384, -1536, -61442. Find an equation for the nth term of the arithmetic sequence.-15, -6, 3, 12, ... A) an = -15 + 9(n + 1) B) an = -15 x 9(n - 1) C) an = -15 + 9(n + 2) D) an = -15 + 9(n - 1)3. Find an equation for the nth term of the arithmetic sequence.a14 = -33, a15 = 9 A) an = -579 + 42(n + 1) B) an = -579 + 42(n - 1) C) an = -579 - 42(n + 1) D) an = -579 - 42(n - 1)4. Determine whether the sequence converges or diverges. If it converges, give the limit. 48, 8, four divided by three , two divided by nine , ... A) Converges; two hundred and eighty eight divided by five B) Converges; 0 C) Diverges D) Converges; -124325. Find an equation for the nth term of the sequence.-3, -12, -48, -192, ... A) an = 4 • -3n + 1 B) an = -3 • 4n - 1 C) an = -3 • 4n D) an = 4 • -3n6. Find an equation for the nth term of a geometric sequence where the second and fifth terms are -21 and 567, respectively. A) an = 7 • (-3)n + 1 B) an = 7 • 3n - 1 C) an = 7 • (-3)n - 1 D) an = 7 • 3n7. Write the sum using summation notation, assuming the suggested pattern continues.5 - 15 + 45 - 135 + ... A) summation of five times three to the power of the quantity n plus one from n equals zero to infinity B) summation of five times negative three to the power of n from n equals zero to infinity C) summation of five times three to the power of n from n equals zero to infinity D) summation of five times negative three to the power of the quantity n plus one from n equals zero to infinity8. Write the sum using summation notation, assuming the suggested pattern continues.-9 - 3 + 3 + 9 + ... + 81 A) summation of the quantity negative nine plus six n from n equals zero to fifteen B) summation of negative fifty four times n from n equals zero to fifteen C) summation of negative fifty four times n from n equals zero to infinity D) summation of the quantity negative nine plus six n from n equals zero to infinity9. Write the sum using summation notation, assuming the suggested pattern continues.64 + 81 + 100 + 121 + ... + n2 + ... A) summation of n squared from n equals eight to infinity B) summation of n minus one squared from n equals eight to infinity C) summation of n squared from n equals nine to infinity D) summation of n plus one squared from n equals eight to infinity10. Find the sum of the arithmetic sequence.17, 19, 21, 23, ..., 35 A) 260 B) 179 C) 37 D) 16011. Find the sum of the geometric sequence. 1, one divided by two, one divided by four, one divided by eight, one divided by sixteen A) one divided by twelve B) 93 C) negative one divided by forty eight D) thirty one divided by sixteen12. An auditorium has 30 rows with 10 seats in the first row, 12 in the second row, 14 in the third row, and so forth. How many seats are in the auditorium? A) 1170 B) 735 C) 1230 D) 60013. Use mathematical induction to prove the statement is true for all positive integers n.The integer n3 + 2n is divisible by 3 for every positive integer n.14. A certain species of tree grows an average of 3.8 cm per week. Write an equation for the sequence that represents the weekly height of this tree in centimeters if the measurements begin when the tree is 5 meters tall.
Accepted Solution
A:
These are 14 questions and 14 answers.
Since this exceeds the limit and I had to delete the last questions and I copied all the answers to a file that is attache. See the attachment with all the answers.
1) Question 1. Find the first six terms of the sequence: a1 = -6, an = 4 • an-1
which means summation of the quantity negative nine plus
six n from n equals zero to fifteen.
9) Question 9.
Write the sum using summation notation, assuming the suggested pattern
continues.
64 + 81 + 100 + 121 + ... + n2 + ...
Answer: A) summation of n squared from n equals eight to infinity
Explanation:
64 = 8^2 81 = 9^2 100 = 10^2121 = 11^2 n^2
=> ∞ ∑ n^2 n=8
which means summation of n squared from n equals eight to
infinity
10) Question 10. Find the sum of the arithmetic sequence.
17, 19, 21, 23, ..., 35
Answer: 260
Explanation: The difference is 2: The sum is: 17 + 19 + 21 + 23 + 25 + 27 + 29 + 31 + 33 + 35. You can use the formula for the sum of an arithmetic sequence:
(A1 + An) * n / 2 = (17 + 35)*10/2 = 260
11) Question 11. Find the sum of the geometric sequence.
1, 1/2, 1/4, 1/8, 1/16Answer: option D) 31/16 Explanation:
You can either sum the 5 terms or use the formula for the partial sum of a geometric sequence. The formula is: Sum = A * ( 1 - r^n) / (1 - r)
Here A = 1, r = 1/2, and n = 5 => Sum = 1 * (1 - (1/2)^5 ) / (1 - 1/2) =