The 8th term is 192 and the common ratio is 2. From the 8th term to the 12th term there are four steps. Therefore, t12 equals 192 multiplied by 2 four times, giving 3072.
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With initial salary of 5,00,000 and annual increment of 20,000, his earnings form an AP. Solving 7,00,000 = 5,00,000 + (n – 1) x 20,000 gives n = 11, meaning his income reaches 7,00,000 after 10 years.
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 = ...
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.