1. Consider the following sequence 8, 10, 12,…, n, (n even). (i) How many terms
ID: 3821351 • Letter: 1
Question
1. Consider the following sequence
8, 10, 12,…, n, (n even).
(i) 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) Compute the exact sum of the terms in the sequence in terms of n.
2. Consider the following functions of n.
f1(n) = n2.
f2(n) = n2 + 1000n.
f3(n) = n, if n is odd,
= n3, if n is even.
f4(n) = n, if n £ 100,
= n3, if n > 100.
(ii) Circle one of True or False in the following questions.
f1(n) = O (f2(n)), True or False
f2(n) = (f1(n), True or False
f3(n) = W (f4(n)), True or False
f3(n) = W (f1(n)), True or False
f4(n) = W (f1(n)) True or False
Explanation / Answer
(i) How many terms are in the sequence? Your answer must be in terms of n. (Count the terms starting with 1 and not 0.)
There are (n/2) - 3 Terms where n starts from 8
If n=8, then 1 term.
if n=10 , then 2 terms
ii) Compute the exact sum of the terms in the sequence in terms of n.
Its equal to 2(n+3)
=> 2n + 6
=> n(n+1) + 6n
=> n2 + 7n
2) f1(n) = O (f2(n)), True or False
f2(n) = (f1(n), True or False
f3(n) = W (f4(n)), True or False
f3(n) = W (f1(n)), True or False
f4(n) = W (f1(n)) True or False
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