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(i) Write down the next two terms of the sequence. (ii) Find, in terms of n, a formula for the nth term of the sequence. (iii) Hence, find the 200th term. A. (i) 30, 34 (ii) 10 + 4n (iii) 804 B. (i) 28, 32 (ii) 10 + 2n (iii) 408 C. (i) 24, 28 (ii) 12 + 4n (iii) 808 D. (i) 26, 30 (ii) 8 + 2n (iii) 404

1 Answer

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(i) The given sequence is 10, 14, 18, 22, which is an arithmetic sequence. An arithmetic sequence is one in which the difference between successive terms is constant. Here, the constant difference is 14 - 10 = 4. To find the next two terms of the sequence, we just add the constant difference to the last term given. So, the next term is 22 + 4 = 26 and the term after that is 26 + 4 = 30. Therefore, the next two terms are 26 and 30.

(ii) The formula for the nth term of an arithmetic sequence is given by a + (n - 1)d, where a is the first term and d is the common difference of the sequence. Here, the first term a is 10 and the common difference d is 4. Substituting these values into the formula gives us the nth term as 10 + 4(n - 1). However, we simplify this to 6 + 4n.

(iii) To find the 200th term, we just need to substitute n = 200 into the formula we have established for the nth term. Doing so gives us 6 + 4 * 200 = 806. Therefore, the 200th term of the sequence is 806.

So the answer is choice B: (i) 26, 30 (ii) 6 + 4n (iii) 806.

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User BrokenGlass
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