write an equation to decribe the sequence below. use n to represent the position of a term in the sequence, where n=1 for the first term
10,-20,40,...
write your answer using decimals and integers
The sequence is alternating between positive and negative terms, where each term is double the absolute value of the previous term.
The equation that represents this sequence is:
aₙ = (-1)^(n+1) * 10 * 2^(n-1)
In this equation, (-1)^(n+1) alternates between -1 and 1, (-1)^(n+1) = -1 when n is odd, and (+1) when n is even. Multiplying by 10 gives the absolute value, and multiplying by 2^(n-1) gives the doubling effect.
For example, when n = 1, a₁ = (-1)^(1+1) * 10 * 2^(1-1) = 10 * 1 * 1 = 10
When n = 2, a₂ = (-1)^(2+1) * 10 * 2^(2-1) = -10 * 10 * 2 = -20
When n = 3, a₃ = (-1)^(3+1) * 10 * 2^(3-1) = 10 * 100 * 4 = 40
So, the sequence is 10, -20, 40,...