11/21/2023 0 Comments Arithmetic sequences and seriesThe ‘nth’ term of this geometric sequence, indicated as ‘an’, can be calculated using the formula: an = a × r^(n – 1).įor the finite geometric series (the sum of the initial ‘n’ terms), denoted as ‘Sn’, the calculation is as follows: Sn = a × (1 – r^n) / (1 – r). Let’s examine the geometric sequence consisting of a, ar, ar², ar³, and so on, where ‘a’ is the initial term and ‘r’ signifies the common ratio. ![]() The total sum of the arithmetic series, denoted as ‘Sn’, can be calculated through the formula: Sn = n/2 (2a + (n – 1) d) (or) Sn = n/2 (a + an).Īlso Check – Quadrilaterals Formula Geometric Sequence and Series Formulas The ‘nth’ term of this arithmetic sequence, represented as ‘an’, can be computed using the formula: an = a + (n – 1) d. Here, ‘a’ signifies its initial term, and ‘d’ stands for its constant difference. Let’s ponder upon the arithmetic sequence denoted by a, a+d, a+2d, a+3d, a+4d, …. Some of the most common examples of sequences are:ĭownload PDF Sequence and Series Formula Arithmetic Sequence and Series Formulas Now, let’s examine each of these formulas closely and gain a comprehensive understanding of the significance of each variable.Īlso Check – Linear Equation Formula Types of Sequence and Series The visual representation below displays all the formulas for sequences and series. In contrast, a harmonic sequence exhibits an arithmetic sequence relationship among the reciprocals of its terms. A geometric sequence features a uniform ratio between successive terms.
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