Arithmetic sequence formula for the nth term. Enter your terms and instantly find the next numbers and the sequence formula. This involves examining numerical or visual patterns, identifying the common difference or ratio, and constructing algebraic expressions that generate any term in the sequence. You can also solve for the common difference from two known terms. An arithmetic sequence has a constant difference between consecutive terms, while a geometric sequence has a constant ratio. If we know the first term of the sequence (denoted by 'a') and the common difference ('d'), we can determine any term in the sequence using this formula. Find the common difference by subtracting any term in the sequence from the term that comes after it. By providing instant calculations of nth terms, sums, and complete sequence lists, it simplifies complex computations and ensures accuracy. The formula for the nth term of an arithmetic sequence is: a n = a 1 + (n-1)d, where a 1 is the first term, d is the common difference and a n is the nth term of the sequence. First, let's examine the relationship between consecutive terms to determine if it's an arithmetic or geometric sequence. Then use the formula to find the 4th term a4 . In cases that have more complex patterns, indexing is usually the preferred notation. Indexing involves writing a general formula that allows the determination of the nth term of a sequence as a function of n. Jan 27, 2026 · The formula for the nth term of an arithmetic sequence is an =a1+(n−1)d. At the end you’ll find nth term worksheets based on Edexcel, AQA and OCR exam questions, along with further guidance on where to go next if you’re still stuck. To find a given term, substitute the corresponding value of n into the nth term formula. You’ll learn what the nth term is and how to work it out from number sequences and patterns. Understand the Arithmetic Sequence Formula & identify known values to correctly calculate the nth term in the sequence. . Use the Number Sequence Calculator to identify patterns in arithmetic, geometric, and Fibonacci sequences. For example, if the nth term is 3n + 2, the 10th term of the sequence can be found by substituting n = 10 into the nth term. Students work with both arithmetic sequences (constant addition) and geometric sequences (constant multiplication The Sequence Calculator is an indispensable tool for students, educators, and professionals dealing with arithmetic and geometric sequences. Results include a breakdown chart and a terms table showing each value in the sequence. 1 day ago · Recall the explicit formula for an arithmetic sequence: an = a1 + (n − 1)d. Jul 23, 2025 · The arithmetic sequence formula is a way to describe the n-th term of an arithmetic sequence. d = 4 We are given the sequence 11,13,15,… and asked to find a formula for its n -th term. In Algebra II, students analyze patterns to determine explicit formulas for the nth term of sequences. Feb 16, 2026 · The formula for the nth term of an arithmetic sequence is: an = a1+(n−1)d where: an is the nth term, a1 is the first term, d is the common difference, n is the term number. 5 days ago · This lesson note on Arithmetic Progression for SSS 2 covers meaning of sequences, nth term, arithmetic mean and sum, with practical problem solving. Given the sequence: -2, 3, 8, First term a1 = −2 We can find d by subtracting the first term from the second term. 3 × 10 + 2 = 32 and so, the tenth term of the sequence is 32. Step 3: Substitute the values of a1 and d into the nth term formula to find the nth term rule. Substitute the first term a1 = 36 and common difference d = 8 into the formula. 16 hours ago · Study with Quizlet and memorize flashcards containing terms like Progression, Progression, Arithmetic Sequence and more. The n^th term is calculated by the formula a_n = a_1+ (n-1)d and the sum is calculated by the formula S_n = (n/2) (2a_1+ (n-1)d). The nth term is a formula used to generate any term of a sequence. The nth The arithmetic sequence formula is used to find the n^th term and the sum of the sequence. Arithmetic Sequence An arithmetic sequence is a number sequence in which the difference between each successive term remains constant. a 2 a 1 = 79 75 = 4 a 3 a 2 = 83 79 = 4 a 4 a 3 = 87 83 = 4 a 5 a 4 = 91 87 = 4 a 6 a 5 = 95 91 = 4 a 7 a 6 = 99 95 = 4 a 8 a 7 = 103 99 = 4 The difference of the sequence is constant and equals the difference between two consecutive terms. The arithmetic sequence calculator finds the nᵗʰ term and the sum of a sequence with a common difference. Math Arithmetic Sequence Calculator Arithmetic Sequence Calculator Enter your sequence's first term (a₁), common difference (d), and term index (n) to find the nth term and the sum of the first n terms of any arithmetic sequence.