![]() Therefore, the recursive formula for the given geometric sequence with starting value 5 and common ratio 4 is a 1 = 5 a n = a n − 1 ⋅ 4, and the explicit formula is a n = 5 ⋅ 4 n − 1. Using this explicit formula, we can directly find any term of the sequence without having to calculate the previous terms. ![]() Substituting the value of a 1 as 5 and the value of r as 4, we get: To find the n t h term of the sequence, we can use the explicit formula: Explanation: A geometric series is of the form. Using this recursive formula, we can find any term of the sequence by multiplying the previous term by 4. Recursive formula for a geometric sequence is an an1 × r, where r is the common ratio. Substituting the value of r as 4, we get: For example, suppose the common ratio is 9. Each term is the product of the common ratio and the previous term. A recursive formula allows us to find any term of a geometric sequence by using the previous term. To find the n t h term of the sequence, we can use the recursive formula: Explicit Formulas for Geometric Sequences Using Recursive Formulas for Geometric Sequences. ![]() Given the starting value a 1 as 5 and the common ratio r as 4, we can write the explicit and recursive formulas for this geometric sequence as follows: Geometric sequence: A sequence of numbers in which each term after the first is found by multiplying the previous term by a fixed value, called the common ratio. To write the explicit and recursive formulas for a given geometric sequence, we need to know its starting value and common ratio.
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