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Consider the sequence $a_1 = 2, a_2 = 5, a_3 = 9, a_4 = 14,$ etc... (a) The recurrence relation is: $a_1 = 2$ and $a_n = a_{n - 1} + (n + 1) \; \forall \;n \in [\mathbb{Z \geq 2}]$. (b) Conjecture an explicit formula for $a_n$.
Free sequence calculator - step-by-step solutions to help identify the sequence and find the nth term of arithmetic and geometric sequence types.
Stan H. Answer by 0123456 (1) ( Show Source ): You can put this solution on YOUR website! Общий член: An= (n^2+3*n)/2.
Learn how to find explicit formulas for arithmetic sequences. For example, find an explicit formula for 3, 5, 7,... Before taking this lesson, make sure you are familiar with the basics of arithmetic sequence formulas.
We are given the following explicit formula of an arithmetic sequence. d ( n) = 5 + 16 ( n − 1) This formula is given in the standard explicit form A + B ( n − 1) where A is the first term and that B is the common difference. Therefore, the first term of the sequence is 5. .
So for n=4, first use the equation f(n) = 12 - 7(n - 1), plug in 4 for n. Then, in the parenthesis, you will have 4-1, which is 3. Then, multiply 7*3 = 21. Lastly, subtract 12 from 21, to get -9, which is the correct answer. When using arithmetic sequence formula.
6 Οκτ 2021 · Use the formula for the \(n\)th partial sum of an arithmetic sequence \(S_{n}=\frac{n\left(a_{1}+a_{n}\right)}{2}\) and the formula for the general term \(a_{n}=a_{1}+(n-1) d\) to derive a new formula for the nth partial sum \(S_{n}=\frac{n}{2}\left[2 a_{1}+(n-1) d\right]\).
