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Write the first six terms of the sequence.$a_n=5^{n-1}$an​=5n−1​, , ,

Question

Write the first six terms of the sequence.an=5n−1a_n=5^{n-1}an​=5n−1​, , ,

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Solution

Sure, here are the first six terms of the sequence an=5n−1a_n=5^{n-1}:

  1. For n=1, a1=51−1=50=1a_1=5^{1-1}=5^0=1
  2. For n=2, a2=52−1=51=5a_2=5^{2-1}=5^1=5
  3. For n=3, a3=53−1=52=25a_3=5^{3-1}=5^2=25
  4. For n=4, a4=54−1=53=125a_4=5^{4-1}=5^3=125
  5. For n=5, a5=55−1=54=625a_5=5^{5-1}=5^4=625
  6. For n=6, a6=56−1=55=3125a_6=5^{6-1}=5^5=3125

So, the first six terms of the sequence are 1, 5, 25, 125, 625, 3125.

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