# Here are the first four terms of a quadratic sequence: 11 26 45 68. Work out an expression for the nth term.

Firstly we must count the values between each of the terms to find the first differences. (EG- 26-11=15, 1st differences: 15,19,23)Next we need to count the values between each of the first differences to find the second differences. (EG- 19-15=4, 2nd differences: 4,4)By halving our second difference we know the number that goes before X^2 in our quadratic sequence. (EG- 4/2=2, our nth term therefore contains 2n^2)We must then compare our sequence to 2n^2, by first calculating 2n^2 in a table of values. (EG- n=1 2n^2=2, n=2 2n^2=8, n=3 2n^2=18, n=4 2n^2=32). Then finding the value between 2n^2 and our sequence (EG- 11-2=9, our values: 9,18,27,36 )Finally to find the part of our nth term after 2n^2 we must find the pattern in our final sequence 9,18,27,36. Which by looking at we know is just the 9 times table which would have an nth term of 9n. Therefore our nth term and final answer is 2n^2 +9n.

Answered by Daniel C. Maths tutor

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