Problem

Find the indicated term for the geometric sequence with first term, $a_{1}$, and common ratio, $r$. Find $a_{98}$, when $a_{1}=47, r=1$. \[ a_{98}= \]

Solution

Step 1 :We are given a geometric sequence with the first term, \(a_{1} = 47\), and the common ratio, \(r = 1\). We are asked to find the 98th term of the sequence, \(a_{98}\).

Step 2 :In a geometric sequence, the nth term can be found using the formula \(a_{n} = a_{1} * r^{(n-1)}\).

Step 3 :Substituting the given values into the formula, we get \(a_{98} = 47 * 1^{(98-1)}\).

Step 4 :Since any number raised to the power of 0 is 1, we simplify the expression to get \(a_{98} = 47 * 1 = 47\).

Step 5 :Final Answer: The 98th term of the geometric sequence is \(\boxed{47}\).

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Source: https://solvelyapp.com/problems/jtDevgay7V/

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