The two-digit numbers divisible by 3 range from 12 to 99, forming an AP with common difference 3. There are 30 such numbers and applying the arithmetic sum formula gives a total sum of 1665.
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Given a + 2d = 12 and a + 49d = 106, solving these simultaneous equations yields first term a = 8 and common difference d = 2. Therefore, the 29th term evaluates to 8 + 28 x 2 = ...
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 ...
Here, first term is 21 and common difference is -3. Solving tn = a + (n – 1)d shows that -81 is the 35th term, and 0 is indeed the 8th term since n is a positive integer.
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.