Find a formula for the n th term of the geometric sequence. Assume that n begins with 1. $a_{1}=10, a_{2}=2$

A) $n−1a_{n}=10\left(\frac{1}{5}\right) ^{n-1}$
B) $a_{n}=2^{n-1}$
C) $a_{n}=2(5) ^{n-1}$
D) $a_{n}=2(5) ^{n}$
E) $xa_{n}=10\left(\frac{1}{5}\right) ^{x}$

Question

Find a formula for the n th term of the geometric sequence. Assume that n begins with 1.

a_{1}=10, a_{2}=2

A)

n−1a_{n}=10\left(\frac{1}{5}\right) ^{n-1}

B)

a_{n}=2^{n-1}

C)

a_{n}=2(5) ^{n-1}

D)

a_{n}=2(5) ^{n}

E)

xa_{n}=10\left(\frac{1}{5}\right) ^{x}

Jason Peter · Accepted Answer

Final Answer : A, Explanation :   Since it is a geometric sequence, we know that the ratio between consecutive terms is constant. Let's call this ratio r. Thus, we have:  \frac{a_{2}}{a_{1}} = r \Rightarrow \frac{2}{10} = r \Rightarrow r = \frac{1}{5}  Now we can use this ratio to find the n-th term:  a_{n} = a_{1}r^{n-1} = 10\left(\frac{1}{5}\right)^{n-1}  Therefore, choice A is the correct answer.

Find a formula for the n th term of the geometric sequence. Assume that n begins with 1. $a_{1}=10, a_{2}=2$

A) $n−1a_{n}=10\left(\frac{1}{5}\right) ^{n-1}$
B) $a_{n}=2^{n-1}$
C) $a_{n}=2(5) ^{n-1}$
D) $a_{n}=2(5) ^{n}$
E) $xa_{n}=10\left(\frac{1}{5}\right) ^{x}$

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