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What is the sum of the first 22 odd numbers?
The sum of a sequence is given by sum = n/2(2a + (n-1)d) where: n = how many a = first number of sequence d = difference between terms of sequence. For the first 22 odd numbers these are: n = 22 a = 1 d = 2 → sum = 22/2(2×1 + (22 - 1)×2)) = 22² = 484 The sum of the first n odd numbers is always n²: sum = n/2(2×1 + (n-1)2) = n/2(1 + (n-1))×2 = n(n) = n²
How can you tell if a infinite geometric series has a sum or not?
The geometric series is, itself, a sum of a geometric progression. The sum of an infinite geometric sequence exists if the common ratio has an absolute value which is less than 1, and not if it is 1 or greater.
What is the formula to find sum of n odd numbers?
The set of odd numbers is an arithmetic sequence. Let say that the sequence has n odd numbers where the first term is a1 and the last one is n. The formula to find the sum on nth terms for an arithmetic sequence is: Sn = (n/2)(a1 + an) or Sn = (n/2)[2a1 + (n - 1)d] where d is the common difference that for odd numbers is 2. Sn = (n/2)(2a1 + 2n - 2)
What is the pattern rule for 1-1-2-3-5-8-13-21-34 pattern?
This is the famous fibonacci sequence, where each term in the sequence is the sum of the previous two. Fn=Fn-1 + Fn-2 F0 = 1 and F1 = 1 are the initial values to begin the sequence. F2 = F1 + F0 = 1 + 1 = 2 F3 = F2 + F1 = 2 + 1 = 3 and so on
What is a sequence that is predictable?
A deterministic sequence - as opposed to a stochastic or random sequence.
