This is a sequence: 2,4,7,11,16. Find the Nth term

1/2n2 + 1/2n + 1

This is a hard one and maybe closer to a maths challenge question. It is easier to explain in person.

First common difference is 1 then 2 then 3 and so on. The second common difference is 1. As there is a constant second difference we know the nth term follows the equation an2 + bn + c.

We can then sub 1 into this equation so ax12 + bx1 c = 2       

Therefore : a + b + c = 2 Sub 2 and 3 in to get three equations with three unknowns : 4a + 2b + c = 4  AND  9a + 3b + c = 7

Get everything in terms of c so c = 2 - a - b = 4 - 4a - 2b = 7 - 9a - 3b.   

Comparing two of these equations to each other eliminates c as an unknown for a while eg 2 - a - b = 4 - 4a - 2b becomes b+3a=2

Compare two other equations to get another expression of a and b so : 7 - 9a - 3b = 4 - 4a - 2b  becomes 3=5a+b

We now have 5a+b=3 and 3a+b=2.  We can use a simultaneous equation to minus the latter from the former and end with 2a=1.

Therefore a =1/2 Sub this into 3a+b=2 and we get b = 1/2

if a and b are a half and a+b+c=2 then c=1.

Therefore answer is 1/2n2 + 1/2n + 1

ZF
Answered by Zia F. Maths tutor

23303 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

what is the point of intersection between the lines 3y-4x=12 and 2x=2y+3


Two shops have deals for purchasing pens: "3 for £2" and "5 for £3" . Mr. Papadopoulos wants to buy 30 pens for his class in school, which deal should he use if he wants to spend the least amount of money possible, and how much will he spend?


Why is completing the square useful and how do you do it?


A bag contains only 8 beads. The beads are identical in all respects except colour. 3 of the beads are black and the other 5 beads are white. A bead is taken at random from the bag and not replaced. A second bead is then taken at random from the bag. What


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