Each example shows a little less than the one before – complete the faded steps yourself, using the same two steps every time: find the common difference, then keep adding it. Also answer the check question.
①Example 1fully worked: read it through
Write the next term: $5,\ 8,\ 11,\ 14,\ \ldots$
1Common difference $=$ next $-$ this
difference $=8-5=3$
2Add it on to get the next term
next term $=14+3=17$
Check · How do you find the common difference?
A subtract a term from the next termB add the first two termsC multiply consecutive termsD count the terms
②Example 2fully worked: read it through
Write the next term: $2,\ 9,\ 16,\ 23,\ \ldots$
1Common difference $=$ next $-$ this
difference $=9-2=7$
2Add it on to get the next term
next term $=23+7=30$
Check · What is the term-to-term rule here?
A add $9$B add $7$C multiply by $2$D add $2$
③Example 3you finish the last 1 step
Write the next term: $20,\ 17,\ 14,\ 11,\ \ldots$
1Common difference $=$ next $-$ this
difference $=17-20=-3$
2Add it on to get the next term
next term $=11-3=8$
Check · Why is the difference negative?
A a mistake – differences are always positiveB the sequence is DECREASING, so you subtract each timeC because $20$ is evenD the terms are getting bigger
④Example 4your turn: every step
Write the next term: $4,\ 10,\ 16,\ 22,\ \ldots$
1Common difference $=$ next $-$ this
difference $=10-4=6$
2Add it on to get the next term
next term $=22+6=28$
Check · What would the term AFTER that be?
A $34$B $28$C $30$D $26$
Answers · Sequences & Patterns
Faded examples · Continuing a linear sequence
① Example 1difference $=8-5=3$→next term $=14+3=17$$17$
Check: A: subtract a term from the next term
② Example 2difference $=9-2=7$→next term $=23+7=30$$30$
Check: B: add $7$
③ Example 3difference $=17-20=-3$→next term $=11-3=8$$8$
Check: B: the sequence is DECREASING, so you subtract each time
④ Example 4difference $=10-4=6$→next term $=22+6=28$$28$
mathedup.co.uk · sheet 19YO