2. Find the nth term of the sequences below:123 4d.4 51 22 53 4е.8'11'*

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Answered: . Find the nth term of the sequences…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Please answer both subparts with explanation. I will really upvote
Question 6 * 1 2 3 4 2'22 23 24" Q6) A: Write the nth term of the sequence:
If you were to shade in a n × n square on graph paper, you could do it the boring way with sides parallel to the edge of the paper) or the interesting way, as illustrated below: The interesting thing here, is that a 3 x 3 square now has area 13. Our goal is the find a formula for the area of a n × n (diagonal) square. (a) Write out the first few terms of the sequence of areas (assume a1, a-5, etc) Is the sequence arithmetic or geometric? If not, is it the sequence of partial sums of an arithmetic or geometric sequence? Explain why your answer is correct, referring to the diagonal squares (b) Use your results from part (a) to find a closed formula for the sequence. Show your work. Note, while there are lots of ways to find a closed formula here, you should use partial sums specifically. 6 Bonus: For the sequenc n question 5, find the closed formula in as many interesting ways as you can.
1 9' 16 2 2 Q2: The nth term of the sequence 2, 2 ..... 2n is (a) n2 (b) n2 (c) 5
Question 6 00 3 Find the sum of the series: 5k k 3 1 a) 50 3 b) 100 6. 100 9. 200 3 50
Find sequence a, a=-4 and as = e the nth term of the arHhmetie b.a,=94 ond au=65
Find the values of a,, a,, a,and a, for the following sequences 1-n 1 2) an n! (-1)*** an 2n-1 1) a %3D 3) %3D %3D 2. 2" 5) а, — 2"-1 4) a, =2+ (-1)" 2"
Answer 8 to 11 answer only 8. What is the next term in the sequence 10,7,3,4,−1 ? A.3 B.5 C.4 D.0 9. What is the general term of the geometric sequence 3,−6,12,−24,.... ? A.an=2(−3)n B.an=3(−2)n C.an=3(−2)n−1 D.an=2(3)n−1 10. What is the general term of the sequence whose first five terms are −1,1/2,−1/4,1/8,−1/16 ? A.an=−(−12)n−1 B.an=−(12)n C.an=−(−12)n D.an=(−12)n−1 11. Find the sum of the first 9999 terms of the sequence 5,5,5,5,5,.... ? A.undefined B.500 C.∞ D.495
7
Find the first five terms in sequences with the following nth terms. 2n - 1
Question 13 .... is define by A sequence a0, a1, a2, a3,.. an = 7an-1 – 10an-2, for n > 2 and a=5 and a =16. An, Prove that an = 3 x 2" + 2 x 5" for all integers n > 0. Edit View Insert Format Tools Table
3. The general formula for a sequence is tn = 2tn-1 - n, where t1 = -7. Find the third term

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. Find the nth term of the sequences below: 23 4 d. 2'3'4'5 2 3 4 е. 2 5 8' 11