The first four terms of a sequence are $$4,\ 6,\ 8,\ 10.$$ Find an expression, in terms of $n$, fo

Question

The first four terms of a sequence are $$4,\ 6,\ 8,\ 10.$$ Find an expression, in terms of $n$, for the $n$th term of this sequence. [1] Rectangular arrangements of tiles follow the number pattern shown below. RowCalculation $1$$1(2)+4=6=2(3)$ $2$$2(3)+6=12=3(4)$ $3$$3(4)+8=20=4(5)$ $4$$4(5)+10=30=5(6)$ $10$ $n$ Complete the entries for Row $10$ and Row $n$. [3] Explain whether $182$ is a term in the sequence $$6, 12, 20, 30,…$$ [1] The difference between two consecutive terms in this sequence is $54$. Find the two consecutive terms. [2]

Accepted Answer

(a) $2n+2$ (b)(i) $10(11)+22=132=11(12)$ and $n(n+1)+(2n+2)=(n+1)(n+2)$ (ii) Yes (iii) $702$ and $756$

Row	Calculation
\(1\)	\(1(2)+4=6=2(3)\)
\(2\)	\(2(3)+6=12=3(4)\)
\(3\)	\(3(4)+8=20=4(5)\)
\(4\)	\(4(5)+10=30=5(6)\)
\(10\)
\(n\)

Number Patterns - General Term of a Sequence

Number Patterns - General Term of a Sequence

Solution:

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