Checking and securing understanding of geometric sequences | Maths

Starter quiz

$32-21=11$ , $43-32=11$ and $54-43=11$ shows that there is __________ additive difference between successive terms in this sequence. $21, 32, 43, 54, ...$

a common ✓

an increasing

a decreasing

a non-integer
Which of these sequences are arithmetic?

$2, 4, 6, 8, 10, ...$ ✓

$2, 4, 7, 10, 14, ...$

$2, 4, 8, 16, 32, ...$

$2, 5, 8, 11, 14, ...$ ✓

$2, -5, 8, -11, 14, ...$
Which of the below sequences matches the description "start at $5$ and add four"?

$5,10,15,20,25, ...$

$4,9,14,19,24, ...$

$5,9,13,17,21, ...$ ✓

$4,8,12,16,20, ...$

$5,1,-3,-7,-11, ...$
By what do we have to multiply $13$ to get to $234$ ? ______

'18' ✓
Match the sequences to their descriptions.

$2,4,6,8,10, ...$

⇔

'Start at $2$ and add $2$ ' ✓

$2,4,8,16,32, ...$

⇔

'Start at $2$ and double each time' ✓

$1,2,4,8,16, ...$

⇔

'Start at $1$ and double each time' ✓

$1,2,3,4,5, ...$

⇔

'Start at $1$ and add $1$ ' ✓

$1,3,5,7,9, ...$

⇔

'Start at $1$ and add $2$ ' ✓

$2,0,-2,-4,-6, ...$

⇔

'Start at $2$ and add $-2$ ' ✓
What is the next term in this sequence? $-5, 10, -20, 40,$ ______

'-80' ✓

Arithmetic (linear) sequences have a common additive difference between successive terms and geometric sequences have a common __________ difference between successive terms.

multiplicative ✓

subtractive

doubling
What is the term-to-term rule of this sequence? $4, 12, 36, 108, ...$

$+8$

$+24$

$\times4$

$\times3$ ✓

'Double'
Which of these sequences are geometric?

$3,9,27,81,243, ...$ ✓

$3,9,36,180,1080, ...$

$3,9,15,21,27, ...$

$3,9,21,39,63, ...$

$3,12,48,192,768, ...$ ✓
Which of these are terms in the geometric sequence which starts like this? $1600, 400, 100, ...$

$50$

$25$ ✓

$25\over4$ ✓

$25\over8$

$25\over16$ ✓
What is the missing first term in this geometric sequence? ______ $, 91, 637, 4459, ...$

'13' ✓
What could the missing term in this geometric sequence be? $8,$ ... $,32$

$12$

$16$ ✓

$20$

$-16$ ✓

$24$

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Identifying a common ratio between each term can help us identify a geometric sequence.
Divide each term by its previous consecutive term, if the results are all the same, this is the common ratio.
If there is a common ratio, then the sequence is geometric.

The common multiplier must be a positive integer for the sequence to be geometric.

The multiplier needs to be the same between consecutive terms but it can be any value. Examples of this can be seen in the lesson.

Geometric sequence - A geometric sequence is a sequence with a constant multiplicative relationship between successive terms.
Common ratio - A common ratio is a key feature of a geometric sequence. The constant multiplier between successive terms is called the common ratio.