Question

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 the formula representing an, the nth term of the sequence.

Answer 1

`a_n=4^(n-1)`

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 (the number which is multiplied with a term to get the next term)

• It is given that the first term,
  `a_1`, is 1

• We also can figure out common ratio, r, to be 4 (since it is the number we multiply a term by, to get the next term)

Now plugging in these into the formula gives us:

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

Answer 2

a₁ = 1 = 4⁰

a₂ = 4 =4¹

a₃ =4 x 4=4²

a₄ =4 x 4² =4³
...................
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a(n) = 4⁽ⁿ⁻¹⁾