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From your series $1 + 2 + 4 + 7 + \ ...$ we can see that $s = 1$, $d_1 = 1$, $c = 1$. So you want the $n$th term here, which means we can calculate the sum up to and including $n$ terms then subtract the sum up to and including $n-1$ terms.
31 mar 2017 · In an arithmetic sequence, the difference between a term and its immediately preceding term is always same. Let use see here, 2 − 1 = 1. 4 − 2 = 2. 7 − 4 = 3. 11 − 7 = 4. Here the difference is continuously increasing. Hence, it is not an arithmetic sequence.
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In mathematics, sequences are usually represented by a series of terms, each of which corresponds to a particular position or index in the sequence. For example, 3, 7, 11, 15, ... is a sequence as there is a pattern where each term is obtained by adding 4 to its previous term. What are 4 Types of Sequences? There are many types of sequences.
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Here are three solutions (there can be more!): Solution 1: Add 1, then add 2, 3, 4, ... So, 1+ 1 =2, 2+ 2 =4, 4+ 3 =7, 7+ 4 =11, etc... Rule: xn = n (n-1)/2 + 1. Sequence: 1, 2, 4, 7, 11, 16, 22, ... (That rule looks a bit complicated, but it works) Rule: xn = xn-1 + xn-2 + 1. Sequence: 1, 2, 4, 7, 12, 20, 33, ... Rule: xn = xn-1 + xn-2 + xn-3.
This free number sequence calculator can determine the terms (as well as the sum of all terms) of the arithmetic, geometric, or Fibonacci sequence.
