You are watching: Find the sum of the arithmetic sequence. 17, 19, 21, 23, ..., 35

These are 14 questions and also 14 answers.Because this exceeds the limit and also I had actually to delete the last questions and I replicated all the answers to a record that is attache. See the attachment via all the answers.1) Inquiry 1. Find the initially six terms of the sequence: a1 = -6, an = 4 • an-1 alternative D) -6, -24, -96, -384, -1536, -6144Explanation:A(1) = - 6A(n) = 4 * A(n-1)n A(n)1 - 62 4 * (-6) = - 243 4 * (-24) = - 964 4 * (-96) = - 3845 4 * (-384) = - 15366 4 * ( -1536) = -6144So, the first 6 terms are: -6, - 24, - 96, - 384, - 1536, - 6144.2) Concern 2: Find an equation for the nth term of thearithmetic sequence.-15, -6, 3, 12, ... alternative D) - 15 + 9(n - 1)Explanation: 1. uncover the difference in between the consecutive terms:-6 - (-15) = -6 + 15 = 93 - (-6) = 3 + 6 = 912 - 3 = 9So, the distinction is 9, and also you deserve to discover any type of term adding 9 to the previous.2. Since the initially term is - 15, you have:First term, A1 = - 15 + 9(0) = - 15Second term, A2 = - 15 + 9(1) = - 6Third term, A3 = -15 + 9(2) = - 15 + 18 = 3Fourth term, A4 = - 15 + 9(3) = - 15 + 27 = 123. So, the general formula is An = - 15 + 9 (n - 1), which is the option D)3) Inquiry 3. Find an equation for the nth term of the arithmetic sequence A14 = - 33, A15 = 9. option B) An = - 579 + 42(n - 1)Explanation:1) Find the difference: 9 - (-33) = 9 + 33 = 422) A15 = A1 + 42 * (15 - 1) => A1 = A15 - 42(15 - 1)A1 = A15 - 42(14)A1 = 9 - 588 = - 579Therefore, the formula es An = - 579 + 42(n - 1)4) Concern 4. Determine whether the sequence converges ordiverges. If it converges, give the limit. 48, 8, 4/3, 2/9, ... the sequence converges to 288/5Explanation:That is a geometric sequence.The ratio is 1/6: 8/48 = 1/6; (4/3) / 8 = 4/24 = 1/6; (2/9)/(4/3) = 6/36 = 1/6.The convergence criterium is that if |ratio| Then the limit 48 / (1 - 1/6) = 48 / (5/6) = 48*6 / 5 = 288/55) Concern 5. Find an equation for the nth term of the sequence.-3, -12, - 48, -192 - 3 * (4)^(n-1)Explanation: clearly any term (from the second) is the previous term multiplied by 4.The initially term is -3The second term is -3(4) = - 12The 3rd term is -3(4)(4)= - 48The fourth term is - 3 (4)(4)(4) = - 192So, the general formula for the nth term is -3 * 4^ (n-1)6) Question 6. Find an equation for the nth term of a geometricsequence where the second and also fifth terms are -21 and also 567, respectively. An =7 * (-3)^(n-1)Explanation:1) The fith term is the second term * (ratio)^3: A5 = A3 * (r)^32) A5 = 567, A2 = - 21 => r^3 = A5 / A2 = - 567 / 21 = - 27=> r = ∛(-27) = - 33) So the initially term is A1 = A2 / r = -21 / -3 = 74) The basic formula is An =7 * (-3)^(n-1)7) Concern 7. Write the amount using summation notation,assuming the said pattern proceeds.5 - 15 + 45 - 135 + ... option B) summation of 5 times negative three to thepower of n from n amounts to zero to infinityExplanation:5 = 5-15 = 5 (-3)45 = 5(-3)^2-135 = 5(-3)^3=> 5 + 5(-3) + 5(-3)^2 + 5(-3)^3+Using the summation notation that is: ∞∑ (5)(-3)^nn=0Which suggests summation of 5 times negative 3 to thepower of n from n equates to zero to infinity8) Question 8. Write the amount utilizing summation notation,assuming the argued pattern proceeds.-9 - 3 + 3 + 9 + ... + 81 alternative A) summation of the quantity negative nine plussix n from n amounts to zero to fifteenExplanation:Find the difference: -3 - (-9) = - 3 + 9 = 63 - (-3) = 3 + 3 = 69 - 3 = 6First term: - 9Second term: - 9 + 6(1)Third term: - 9 + 6(2)nth term = - 9 + (n -1)Summation = <- 9> + <- 9 + 6(1) + <-9 + 6(2)> + <-9 + 6(3) >+ <-9 + 6(15) >Using summation notation:15∑ <-9 + 6n>n=0which suggests summation of the quantity negative nine plus6 n from n equals zero to fifteenager.9) Concern 9.Write the amount utilizing summation notation, assuming the suggested patterncontinues.64 + 81 + 100 + 121 + ... + n2 + ... A) summation of n squared from n equates to eight to infinityExplanation:64 = 8^2

81 = 9^2

100 = 10^2

121 = 11^2

n^2

=>

∑ n^2

n=8

which implies summation of n squared from n equals eight toinfinity

10) Concern 10.

Find the amount of the arithmetic sequence.17, 19, 21, 23, ..., 35

260

Explanation:

The distinction is 2:

The amount is: 17 + 19 + 21 + 23 + 25 + 27 + 29 + 31 + 33 + 35.

You have the right to usage the formula for the sum of an arithmetic sequence:

(A1 + An) * n / 2 = (17 + 35)*10/2 = 260

11) Concern 11. Find the amount of the geometric sequence.

1, 1/2, 1/4, 1/8, 1/16

alternative D) 31/16

Explanation:

You deserve to either sum the 5 terms or usage the formula for the partial sum of a geometric sequence.