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.






DC
Answered by Daniel C. Maths tutor

13772 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

N sweets in a bag. 6 sweets are orange. The rest are yellow. Hannah takes a random sweet from the bag and eats it. She then takes another random sweet from the bag & eats it. The probability Hannah eats 2 orange sweets is 1/3. Show n^2 - n - 90 = 0.


Solve the simultaneous equations: 3x + 4y = 5 and 2x – 3y = 9


Dominik hires a satellite phone. His total hire charge is £860. For how many weeks did he hire the phone? (Total hire charge = No. of week X 90 +50)


Please expand the following brackets: (x+3)(x+5). Give your answer in its simplest form.


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

MyTutor is part of the IXL family of brands:

© 2025 by IXL Learning