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 = ...
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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.
Area A contains purely aquatic animals: Dolphin and Whale. Area B contains terrestrial animals: Horse, Sheep, Squirrel, Earthworm and Pigeon. Area C includes animals adapted to both land and water: Frog, Crocodile and Tortoise.