Page 3 - Number sequence

Question

Given the sequence: 3; 6; 11; 18; 27; . . .

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

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ii. Hence determine the 13 term.

Solution.
We can tell that the numbers are increasing significantly with the increasing of terms. ∴ we can
say terms are being squared.

Compare 1; 4; 9; 16; 25; . . .
and 3; 6; 11; 18; 27; . . .

Natural numbers are being squared and 2 is added to the results, starting from 1 thus 1² +2 = 3.
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∴ n term = n² + 2
or

Term 1 1² + 2 3

Term 2 2² + 2 6

Term 3 3² + 2 11

Term 4 4² + 2 18

Term 5 5² + 2 17

Term n ² + 2 ² + 2

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th
n term = n² + 2, ∴ 13 = 13² + 2 = 171