High School

State the first five terms of the sequence [tex]a_n = -5^n[/tex], starting from [tex]n = 1[/tex]. Write all five terms on the same line separated by a comma.

a) -5, -25, -125, -625, -3125
b) -5, 25, -125, 625, -3125
c) 5, -25, 125, -625, 3125
d) 5, 25, 125, 625, 3125

Answer :

Final answer:

The first five terms of the sequence aₙ = -5ⁿ are b) -5, 25, -125, 625, -3125. This is a geometric sequence with alternating signs because of the negative base raised to successive powers.

Explanation:

The sequence described by the formula an = -5n represents a geometric sequence where each term is -5 raised to the positive integer power of n. To calculate the first five terms of this sequence starting with n=1, we simply substitute n with 1, 2, 3, 4, and 5, respectively.

  • When n=1: a1 = -51 = -5
  • When n=2: a2 = -52 = 25 (since a negative number raised to an even power is positive)
  • When n=3: a3 = -53 = -125
  • When n=4: a4 = -54 = 625
  • When n=5: a5 = -55 = -3125

Therefore, the first five terms of the sequence are -5, 25, -125, 625, -3125, which corresponds to option b).

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