Write an equation for nth term in the sequence: -2, 5, -10, 17, -26
Tn = (-1)^n * (n^2+1)
Write the nth term of the following sequence in terms of the first term of the sequence.
2, -4, 8, -16, .
To find the equation for the nth term in the given sequence, we need to identify the pattern. Looking at the sequence, we can observe that the sequence alternates between positive and negative numbers and follows a pattern of adding multiples of 3.
The first term, -2, is followed by 5, which is obtained by adding 7 (3 * 2) to -2. Similarly, -10 is obtained by subtracting 15 (3 * 5) from 5. Then 17 is obtained by adding 27 (3 * 9) to -10, and so on.
From this pattern, we can deduce that the nth term in the sequence can be found using the formula:
a_n = (-1)^(n+1) * (3n^2 - 1)
where a_n represents the nth term in the sequence.