# What is the nth term rule for this quadratic sequence? 6, 10, 18, 30?

### VERIFIED

### Sohini Khan

A supportive and engaging tutor with an aim for success

First we make some nth term that almost fits what we have. Almost, because we have to compare our nth term and the question’s nth term to fill in the blanks. So since it’s a quadratic sequence, we have to find the second difference, halve it and stick it in front of the n^2. Our first differences are: 6 (+4) 10 (+8) 18 (+12) 30 Our second differences are: 4 (+4) 8 (+4) 12 So our second difference is 4. Then we halve it and stick the number in front of n^2. This gives us 2n^2. This is our nth term that almost fits. The sequence with nth term 2n^2 has terms: 2, 8, 18, 32. To get from our template sequence to the sequence in the question, we have to: (+4), (+2), (+0) (+-2) These differences form a subsequence: 4, 2, 0, -2, which is linear and has the common difference -2. It has an nth term of -2n + 6. So if we add this onto our template, we should reach the quadratic sequence in the question. This gives us an nth term rule of 2n^2 - 2n + 6. To double check, the terms of this sequence are: 2(1) - 2 + 6, 2(4) - 4 + 6, 2(9) - 6 + 6, 2(16) - 8 + 6 = 6, 10, 18, 30 which is the same as the sequence in the question. A little extra but it’s good peace of mind. Hope that makes sense ~ Sohini

### Sohini also answered

### Asked in Maths 💯

ASKED BY KIARA

MATHS 💯#### How do you find the area of a two-dimensional prism?

Hi Kiara, by definition a prism is three-dimensional. A prism is a type of 3D shape with flat sides. It has at least two ends that are the same shap...

ASKED BY YIGIT

MATHS 💯#### Write the eqaution of the line in the form y=mx+c, q1) which passes through (-5,-2) and (1,0)?

How do we do this? First, find the difference between the two x & y co-ordinates: y² - y¹ = (1 - -5) = 6 x² - x¹ = (0 - -2) = 2 So we now know that ...

ASKED BY HUMAIRA

MATHS 💯#### What is the nth term rule of linear sequence below? 6,13,20,27,34?

• First of all make sure to number (n) your terms (t) in the sequence above • Then work out the difference (d) which Is +7 each time •hence the base...

ASKED BY MIA

MATHS 💯#### What is 300 as a product of prime factors using index notation?

it may be easier to visualise 300 as a product of prime factors using a prime factor tree. 300 / \ 2 150 / \ 2 75 / \ 3 25 / \ 5 5 all the numbers w...

ASKED BY CARTEL

MATHS 💯#### The complex number is defined by w=(22+4i)/(2-i)². Show that w= 2+4i. How to solve this?

Further Maths! <3 Okay so, you need to rationalise the the denominator. But before we do that we should square the complex number (2-i). (2-i)² give...

ASKED BY ANDREEA

MATHS 💯#### A is directly proposional to the square of b. If a=16 when b=2, find the value of a when b=5?

When A is directly proportional to Bsquared, there is also another constant factor involved. We call this constant factor k. Firstly we need to work...

ASKED BY EMMA

MATHS 💯#### The area of a square is 100 cm^2 Work out the area of the circle.Give your answer in terms of pi?

To do this I will assume that the circle is inside the square, touching the sides. area of square = length * width 100 = length * width and since it...

ASKED BY SAHMA

MATHS 💯#### How do you find the nth term of the sequence: 5,14,29,50,77 I got 3n²+2+2. Is that correct?

Simply the answer is incorrect if you substitute n=1 for first term in your equation you’ll get 7 while it should be 5. The correct answer is as fol...

ASKED BY AMBAR

MATHS 💯#### I don’t understand algebra. Help me please. I get stuck and confused at stuff?

Hello Ambar, Algebra, and maths in general, can be quite challenging but there are tricks to get through the difficulties. What works in every case ...

ASKED BY FAITH

MATHS 💯#### Trigonometry - How do you find the special sine, cosine and tangent angles?

You can easily memorise the special angles in a grid (have a look on google) or you can work them out manually buy the use of two triangles. The fir...

Find me a tutor

We take your privacy seriously. View our policy.