Starting with t1 equal to 2, the recursive rule gives the sequence 2, 4, 10, 28, 82, 244, 730. Therefore, 730 occurs at the seventh position. Hence, 730 is the seventh term of the sequence.
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The marble counts represent the sum of the first 25 natural numbers. Using the sum formula Sn = n(n + 1) / 2 with n = 25, the total calculation is 25 x 26 / 2, which gives 325 marbles.
In this sequence, the first term is 11 and common difference is -3. The explicit nth term simplifies to tn = 14 – 3n, while its recursive rule is stated as t1 = 11, tn = tn-1 – 3 for ...
For the given arithmetic progression, the first term is 3 and the common difference is 5. Using the formula tn = a + (n – 1)d, the 10th term is 48 and the 26th term is 128.