Algorithm Analysis Problems #1) Please explain the solution thoroughly it\'s mor
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Question
Algorithm Analysis Problems #1)
Please explain the solution thoroughly it's more important than the answer itself. Here is my class work and a provided link to origonal word document. Thank You.
https://docs.google.com/document/d/1sgmQ24EZxDZL7WfqPh_hjz2MNu2wGGvl47rQrmFeagY/edit?usp=sharing
8, 10, 12 n, (n even). (i) (4 pts) How many terms are in the sequence? Your answer must be in terms of n. (Count the terms starting with 1 and not 0.) (ii) (6 pts) Compute the exact sum of the terms in the sequence in terms of n. 6 r a a t a IO ara d n-6 of terms) (first termExplanation / Answer
STEP1:-
Given Sequence:-
8,10,12,.....,n.
1.Find out the common difference between two consecutive terms.
Let me consider the common difference be d.
Now d = 2.
STEP2:-
2.Find out the first term and the last term from the sequence.
Let me consider the first term be F.
Let me consider the last term be L.
STEP3:-
3.Find out the number of terms from the sequence by using formula.
The formula to find out the number of terms from the sequence is n = (L-F)/d + 1.
where...
n be the number of terms.
F be the first term.
L be the last term.
d be the common difference between consecutive terms.
Now...
n = (n-8)/2 + 1.
n = (n-8+2)/2
n = (n-6)/2
The total number of terms n = (n-6)/2.
2.The Exact sum of the first n terms in the sequence:-
The formula to find the Exact sum of the first n terms of an arithmetic sequence
Sum = n(F + L)/2
where...
sum be the sum of the first n terms in the sequence.
n be the number of terms in the sequence. // we should take from the above problem.
F be the first term in the sequence.
L be the last term in the sequence.
Now...
sum = (n-6)(8+n)
-------------
2*2
sum = 8n+n^2-48-6n
-------------------
4
sum = n^2+2n-48
-------------
4
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