Scelta multipla
Write the first four terms of the following geometric sequence.
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13. Sequences, Series, and the Binomial Theorem
Geometric Sequences
Scelta multipla
Find the indicated term of the following geometric sequence.
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Identify the general term of the geometric sequence given by the formula \(a_{n} = 10 \left( \frac{1}{5} \right)^{n-1}\).
Substitute \(n = 4\) into the formula to find the fourth term \(a_4\): \(a_4 = 10 \left( \frac{1}{5} \right)^{4-1}\).
Simplify the exponent: \(4 - 1 = 3\), so rewrite the term as \(a_4 = 10 \left( \frac{1}{5} \right)^3\).
Calculate the power of the fraction: \(\left( \frac{1}{5} \right)^3 = \frac{1^3}{5^3} = \frac{1}{125}\).
Multiply the coefficient by the fraction: \(10 \times \frac{1}{125} = \frac{10}{125}\), then simplify the fraction to its lowest terms.
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