Question

Write an explicit formula for a, start subscript, n, end subscripta

n
​
, the n, start superscript, th, end superscriptn
th
term of the sequence 64, comma, minus, 16, comma, 4, comma, point, point, .64,−16,4,....

Answer 1

The explicit formula for the nth term (an) in the sequence 64, -16, 4, ... is given by
`\( a_n = (-1)^n * 2^(6-n) \)`, where n is the position in the sequence.

The sequence 64, -16, 4, ... follows a distinct pattern. It begins with 64 and alternates between multiplying by -1 and taking the square root.

To express this pattern in an explicit formula for the nth term (an), we observe that the power of 2 decreases by 1 with each term, and the sign alternates between positive and negative.

The formula is given by
`\( a_n = (-1)^n * 2^(6-n) \)`, where n represents the position of the term in the sequence. This formula encapsulates the alternating multiplication by -1 and the decreasing powers of 2, providing a concise representation of the sequence's terms.

The complete question is:

Write an explicit formula for an, the nth term of the sequence

64, -16, 4,....