Here, a = the first term = 1/4 and the common ratio, r = (1/8) / (1/4) = 1/2. We can find the values of 'a' and 'r' using the geometric sequence and substitute in this formula to find the sum of the given infinite geometric sequence.įor example, Let us find the sum of all terms of the geometric sequence 1/4, 1/8, 1/16. The sum of infinite terms of a geometric sequence whose first term is 'a' and common ratio is 'r' is, a / (1 - r). How To Use the Sum of Geometric Sequence Formula for Infinite Geometric Sequences? Thus, the number of fishes on 5 th day = 76. To find the population of fishes on 5 th day, we have to substitute n = 5 in the n t h term of the geometric sequence formula. In this case, the first term is, a = 1216 and the common ratio is, r = 1/2 (because the fishes become half on every day). If the pond starts with 1216 fishes, what would be the population on the 5 t h day? The geometric sequence formulas have man y applications in many fields such as physics, biology, engineering, also in daily life. Consider the following example.įor example, the population of fishes in a pond every day is exactly half of the population on the previous day. What Are the Applications of Geometric Sequence Formulas? For detailed proof, you can refer to " What Are Geometric Sequence Formulas?" section of this page. To derive the sum of geometric sequence formula, we will first multiply this equation by 'r' on both sides and the subtract the above equation from the resultant equation. Then sum of its first 'n' terms is, S n = a + ar + ar 2 +. How To Derive the Sum of Geometric Sequence Formula?Ĭonsider a geometric sequence with first term 'a' and common ratio 'r'.
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