What is the nth term of 2,6,11,17,24? Thanks
1 Answer
Mar 8, 2018
Explanation:
We can identify this quadratic sequence by the method of differences:
Write down the given sequence:
#color(blue)(2), 6, 11, 17, 24#
Write down the sequence of differences between consecutive terms:
#color(blue)(4), 5, 6, 7#
Write down the sequence of differences of those differences:
#color(blue)(1), 1, 1#
Having reached a constant sequence, we can match the original sequence with a formula using the initial term of each of these sequences as coefficients:
#a_n = color(blue)(2)/(0!)+color(blue)(4)/(1!)(n-1)+color(blue)(1)/(2!)(n-1)(n-2)#
#color(white)(a_n) = 2+4n-4+1/2n^2-3/2n+1#
#color(white)(a_n) = 1/2(n^2+5n-2)#