Page 4 - Number sequence

More examples on rules used in determining terms in a sequence.

Questions

Consider the sequence: 3; 8; 13; 18; 23; . . .

th
i. Write down the general rule for the n term of the sequence

th
ii. Hence calculate the 67 term

Solution
i. 5 is being added to the previous term to get the next term

st
nd
Step 1: Check the difference between 2 term and the 1 term, thus 8−3 = 5.
Step 2: Then introduce n to 5 so that it is 5n.
Step 3: Term 1: n= 1, then 5(1) + = 3
= 3−5
= −2

th
∴ n term = −2 + 5n
or

Term 1 −2 + 5(1) = 3 3

Term 2 −2 + 5(2) = 8 8

Term 3 −2 + 5(3) = 13 13

Term 4 −2 + 5(4) = 18 18

Term 5 −2 + 5(5) = 23 23

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Term n −2 + 5(n) = −2 +5n −2 +5n

th
rd
ii. If the n term = −2 + 5n, then the 23 term = −2 + 5 × 67 = 333