What is the nth term of 2,6,11,17,24? Thanks

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Mar 8, 2018

Answer:

#a_n = 1/2(n^2+5n-2)#

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)#

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