High School

What is the 7th term in the geometric sequence described by this explicit formula?

\[ a_n = 2 \times 5^{n-1} \]

A. 625
B. 3125
C. 15625
D. 78125

Answer :

Final answer:

The correct option is b) 3125. To find the 7th term in a geometric sequence with a given explicit formula involving exponents, substitute n = 7 in the formula and perform the calculation to get the answer as 31250 or 3125 (b).

Explanation:

The 7th term in the geometric sequence represented by the explicit formula aⁿ = 2*5ⁿ⁻¹ is calculated as follows:

  1. Substitute n = 7 into the formula: a⁷ = 2*5^(7-1)
  2. a⁷ = 2*5^6 = 2*15625 = 31250

Therefore, the 7th term in the sequence is 31250. The correct answer is 3125 (b).

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