Question 8 of 51intermediate🔧 ApplyNumerical4 marks

Consider the expression tn=3n−7t_n = 3n - 7. (i) Find its first, second, third, 12th12^{th}, 18th18^{th} and 50th50^{th} terms. (ii) Which term of the sequence is 332? (iii) Is 557 a term of this sequence? Why or why not?

(i)
Answer

First term: t1=3(1)−7=−4t_1 = 3(1) - 7 = -4 Second term: t2=3(2)−7=−1t_2 = 3(2) - 7 = -1 Third term: t3=3(3)−7=2t_3 = 3(3) - 7 = 2 12th term: t12=3(12)−7=29t_{12} = 3(12) - 7 = 29 18th term: t18=3(18)−7=47t_{18} = 3(18) - 7 = 47 50th term: t50=3(50)−7=143t_{50} = 3(50) - 7 = 143

(ii)
Answer

Finding the term: Let the term number be nn.

3n−7=3323n - 7 = 332 3n=332+73n = 332 + 7 3n=3393n = 339 n=113n = 113

332 is the 113th term of the sequence.

(iii)
Answer

Checking the term: Let the term number be nn.

3n−7=5573n - 7 = 557 3n=557+73n = 557 + 7 3n=5643n = 564 n=188n = 188

Since n=188n = 188 is a positive integer, 557 is a term of this sequence.

Explanation

To find specific terms of a sequence given by an explicit formula, we substitute the position number n into the formula. To find which term a specific number represents, we set the formula equal to that number and solve for n. If the resulting value of n is a positive integer, the number is a valid term in the sequence.

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