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Consider the sequence given by an = 2 – 6n. a. Find the first 6 terms of the sequence. What sort of sequence is this? b. Find the sum of the first 55 terms. That is, compute E1 ak. Uso nolunomial ftting to ind clocod formula for tbo coquonco (a,).

Consider the sequence given by an = 2 – 6n. a. Find the first 6 terms of the sequence. What sort of sequence is this? b. Find the sum of the first 55 terms. That is, compute E1 ak. Uso nolunomial ftting to ind clocod formula for tbo coquonco (a,).

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Please help with this discrete math question with details on how to do it. Need help with question #4. Thank you.

4. Consider the sequence given by an = 2 – 6n. a. Find the first 6 terms of the sequence. What sort of sequence is this? b. Find the sum of the first 55 terms. That is, compute E 1 ax. 5. Use polynomial fitting to find a closed formula for the sequence (an)n e N,: 1,3, 11,31, 69, .. 6. Consider the recurrence relation an = an-1 – 2an-2 with first two terms ao = 0 and aj = 1. a. Write out the first 5 terms of the sequence defined by this recurrence relation. b. Solve the recurrence relation. That is, find a closed formula for a,. 7. Prove the following using induction. k3 = 13 + 23 + 33 + ...+ n³ = (1+2 +3 + …·+n)² k=1 n(n+1) [Hint: Recall that 1 + 2 + 3 + ..+n =
Transcribed Image Text:4. Consider the sequence given by an = 2 – 6n. a. Find the first 6 terms of the sequence. What sort of sequence is this? b. Find the sum of the first 55 terms. That is, compute E 1 ax. 5. Use polynomial fitting to find a closed formula for the sequence (an)n e N,: 1,3, 11,31, 69, .. 6. Consider the recurrence relation an = an-1 – 2an-2 with first two terms ao = 0 and aj = 1. a. Write out the first 5 terms of the sequence defined by this recurrence relation. b. Solve the recurrence relation. That is, find a closed formula for a,. 7. Prove the following using induction. k3 = 13 + 23 + 33 + ...+ n³ = (1+2 +3 + …·+n)² k=1 n(n+1) [Hint: Recall that 1 + 2 + 3 + ..+n =
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