Write an explicit formula for $ a_n $, the $ n $th term of the sequence 175, 35, 7, ...

A. $ a_n = 175 \times \left(\frac{1}{5}\right)^{n-1} $

B. $ a_n = 175 \times 5^{-(n-1)} $

C. $ a_n = 175 \times 5^{n+1} $

D. $ a_n = 175 \times \left(\frac{1}{5}\right)^{n+1} $

The nth term of the geometric sequence 175, 35, 7, .... is given by the formula an = 175×(1/5)^(n-1), identifying each term as one-fifth of the preceding term. Therefore, the correct option is: a) an = 175×(1/5)(n-1)

Explanation:

The student has asked for the explicit formula for the nth term of the geometric sequence 175, 35, 7, .... To determine this, we observe that each term is ÷ 5 of the previous term.

This means that the common ratio (r) is ⅕ or 0.2. Using the formula for the nth term of a geometric sequence, which is an = a1 × r(n-1), where a1 is the first term and r is the common ratio, we can substitute a1 = 175 and r = ÷ 5 to get the formula.

The correct formula would then be an = 175×(1/5)(n-1)

Therefore, the correct option is: a) an = 175×(1/5)(n-1)

Write an explicit formula for \( a_n \), the \( n \)th term of the sequence 175, 35, 7, ...A. \( a_n = 175 \times \left(\frac{1}{5}\right)^{n-1} \)B. \( a_n = 175 \times 5^{-(n-1)} \)C. \( a_n = 175 \times 5^{n+1} \)D. \( a_n = 175 \times \left(\frac{1}{5}\right)^{n+1} \)

Answer :

Final answer:

Explanation:

Other Questions

Write an explicit formula for \( a_n \), the \( n \)th term of the sequence 175, 35, 7, ...

A. \( a_n = 175 \times \left(\frac{1}{5}\right)^{n-1} \)

B. \( a_n = 175 \times 5^{-(n-1)} \)

C. \( a_n = 175 \times 5^{n+1} \)

D. \( a_n = 175 \times \left(\frac{1}{5}\right)^{n+1} \)