Question

question 2
find a formula for the general term ( a_n ) of the sequence assuming the pattern of the first few terms continues.
( left{ \frac{10}{2}, \frac{10}{4}, \frac{10}{8}, \frac{10}{16}, \frac{10}{32}, dots
ight} )
assume the first term is ( a_1 ).
( a_n = )
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Explanation:

Step1: Analyze numerator pattern

The numerator of each term is 10, so it's constant: \(10\).

Step2: Analyze denominator pattern

Denominators: \(2, 4, 8, 16, 32, \dots\) which is \(2^1, 2^2, 2^3, 2^4, 2^5, \dots\). For term \(n\), denominator is \(2^n\).

Step3: Form general term

Combine numerator and denominator: \(a_n=\frac{10}{2^n}\).

Answer:

\(\frac{10}{2^n}\)