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Natasha2012 [34]
3 years ago
5

Let the sequence {an} be defined so that a1 = 1 and each succeeding term is found by multiplying the one before it by 4. Find th

e formula representing an, the nth term of the sequence.
Mathematics
2 answers:
Basile [38]3 years ago
7 0

Answer:

a_n=4^{n-1}


Step-by-step explanation:


When each term is multiplied by a number to get the next term, it is a geometric sequence.

The general term (nth term) of a geometric sequence is given by the formula:

a_n=a_1*r^{n-1}

Where a_1 is the first term and r is the common ratio <em>(the number which is multiplied with a term to get the next term)</em>

  • It is given that the first term, a_1, is 1
  • We also can figure out common ratio, r, to be 4 <em>(since it is the number we multiply a term by, to get the next term)</em>

<em>Now plugging in these into the formula gives us:</em>

a_n=a_1*r^{n-1}\\a_n=(1)*(4)^{n-1}\\a_n=4^{n-1}

Anika [276]3 years ago
5 0
A₁ = 1 = 4⁰

a₂ = 4 =4¹

a₃ =4 x 4=4²

a₄ =4 x 4² =4³
...................
...................

a(n) = 4⁽ⁿ⁻¹⁾
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