Justifying terms of a sequence | Maths | Quizalize & Oak National Academy

Starter quiz

The calculation 6(20) - 8 would find the 20 $^\text{th}$ ______ of the sequence $6n-8$ .
- 'term' ✓
Which of these describe features of the sequence $5n-9$ ?
- It has a constant difference of +5 ✓
- It decreases by 9 each time
- The terms always end in the digits 1 or 6
- The positive terms always end in the digits 1 or 6 ✓
- It starts at -4 ✓
What is the 75 $^\text{th}$ term of the sequence $6n-17$ ?
- 675 - 17 = 658
- 6 + (75) - 17=64
- 6(75) - 17 = 450 - 17 = 433 ✓
- (6 - 17)75 = -11 $\times$ 75 = -825
What happens when you plot an arithmetic sequence?
- You get a straight line of values. ✓
- You get a decreasing pattern of values.
- You get a curve.
- You might see points in two quadrants. ✓
- You might plot points in all four quadrants.
Calculate the 200 $^\text{th}$ term of $17.96-0.32n$ . You may use a calculator.
- 81.96
- 3528
- -81.96
- -46.04 ✓
Put these term values in order of size. Start with the smallest.
- 1
  
  ⇔
  
  The 80 $^\text{th}$ term of the sequence $6n-35$
- 2
  
  ⇔
  
  The 50 $^\text{th}$ term of the sequence $596-3n$
- 3
  
  ⇔
  
  The 60 $^\text{th}$ term of the sequence $9n-88$
- 4
  
  ⇔
  
  The 95 $^\text{th}$ term of the sequence $5n-11$
- 5
  
  ⇔
  
  The 50 $^\text{th}$ term of the sequence $9n+19$

The sequence 37, 47, 57, 67, 77, ... could be described as which?
- Linear ✓
- Non-linear
- Arithmetic ✓
- Increasing ✓
- Decreasing
Which of the below statements supports the justification that 6941 is not in the arithmetic sequence starting 14, 19, 24, 29, 34, ...?
- It's too large a number.
- 14, 19, 24, 29, 34, ... is a translation of a $5n$ sequence. ✓
- The sequence will always end in the digit 4 or 9 in the ones position. ✓
- 6941 is an odd number, and the sequence begins with an even number.
Which of the below will be common terms in the sequences $2n+24$ and $5n+13$ ?
- 13 048 ✓
- 103
- 888 ✓
- 1001
- 8008 ✓
The first 8 terms of a sequence are plotted. Which term is incorrect in the plotting of this arithmetic sequence?
- The 2 $^\text{nd}$ term
- The 4 $^\text{th}$ term
- The 6 $^\text{th}$ term ✓
- The 8 $^\text{th}$ term
Which of the below is a useful estimation to start with when trying to find 315 in the sequence $6n-9$ ?
- $n=25$
- $n=50$ ✓
- $n=100$
- $n=300$
- $n=600$
What does this calculator display tell us?
- 881 is in the sequence $8n-17$
- 881 is not in the sequence $8n-17$ ✓
- 881 is the 112.25 $^\text{th}$ term.
- 881 is not a term because 112.25 is not a whole number. ✓

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It is impossible to tell if 174 368 is in the sequence -8,-3,2,7, ...

Generalising the rule for forming a given sequence can help us see if a value is in the sequence.

Arithmetic sequence - An arithmetic (or linear) sequence is a sequence where the difference between successive terms is a constant.