geometric sequence examples with solutions

Geometric sequence examples with solutions how to#

Geometric sequence examples with solutions how to#

How To Derive the Sum of Geometric Sequence Formula?Ĭonsider a geometric sequence with first term 'a' and common ratio 'r'. The sum of infinite geometric sequence = a / (1 - r).Then we get:Īnswer: The 10 th term of the given geometric sequence = 19,683.Įxample 2: Find the sum of the first 15 terms of the geometric sequence 1, 1/2, 1/4, 1/8. To find the 10 th term, we substitute n = 10 in the above formula. Using the geometric sequence formula, the n th term of a geometric sequence is, Note: Here, r = the ratio of any two consecutive terms = a n/a n-1.Įxamples Using Geometric Sequence FormulasĮxample 1: Find the 10 th term of the geometric sequence 1, 3, 9, 27. S n = a (1 - r n) / (1 - r), when |r| 1 (or) when r 1, the infinite geometric sequence diverges (i.e., we cannot find its sum). The sum of the first 'n' terms of the geometric sequence is, Similarly we can derive the other formula (S n = a (r n - 1) / (r - 1). Subtracting the equation (2) from equation (1), Then sum of its first 'n' terms of the geometric sequence a, ar, ar 2, ar 3. Sum of n Terms of Geometric Sequence Formula The n th term of the geometric sequence is, a n = a

Its first term is a (or ar 1-1), its second term is ar (or ar 2-1), its third term is ar 2 (or ar 3-1). We have considered the sequence to be a, ar, ar 2, ar 3. Let us see each of these formulas in detail. Here are the geometric sequence formulas. We will see the geometric sequence formulas related to a geometric sequence with its first term 'a' and common ratio 'r' (i.e., the geometric sequence is of form a, ar, ar 2, ar 3. We can also find the sum of infinite terms of a geometric sequence when its common ratio is less than 1. The geometric sequence formulas include the formulas for finding its n th term and the sum of its n terms.