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In this activity, we will work out some of the terms of a sequence from a rule known as a T formula.
Example
Find the first 5 terms in the sequence given by the formula:
Tn = 50 - 4n2
where n is the position of the term in the sequence.
Additionally find the 20th term and the 100th term.
Answer
We get the first term, T1, by substituting n = 1 into the T formula.
We get the second term, T2, by substituting n = 2 into the T formula... etc....
So...
1st term T1 = 50 - 4 × 12 = 50 - 4 × 1 = 50 - 4 = 46
2nd term T2 = 50 - 4 × 22 = 50 - 4 × 4 = 50 - 16 = 34
3rd term T3 = 50 - 4 × 32 = 50 - 4 × 9 = 50 - 36 = 14
4th term T4 = 50 - 4 × 42 = 50 - 4 × 16 = 50 - 64 = -14
5th term T5 = 50 - 4 × 52 = 50 - 4 × 25 = 50 - 100 = -50
Now we find the 20th and 100th terms.
T20 = 50 - 4 × 202 = 50 - 4 × 400 = 50 - 1,600 = -1,550
T100 = 50 - 4 × 1002 = 50 - 4 × 10,000 = 50 - 40,000 = -39,950
Let's practise this in the following questions.
Question
/ 10Mr Shepherd
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Teacher explanation