Exercise 8.2

Find the \(10^{th}\) and \(26^{th} \) terms of the AP: 3, 8, 13, 18,...

Which term of the AP: 21, 18, 15,... is −81? Also, is 0 a term of this AP? Give reasons for your answer.

Find the \(n^{th}\) term of the AP: 11, 8, 5, 2,... Write the recursive rule for this AP.

An AP consists of 50 terms in which the \(3^{rd}\) term is 12 and the last term is 106. Find the \(29^{th}\) term. (Hint: If 'a' is the first term and 'd' the common difference, then we arrive at the equations a + 2d = 12 and a + 49d = 106. Solve this pair of linear equations for 'a' and 'd'.)

How many 2-digit numbers are divisible by 3? What is the sum of all these 2-digit numbers?

Harish started work at an annual salary of ₹5,00,000 and received an increment of ₹20,000 each year. After how many years did his income reach ₹7,00,000?

A child arranges marbles in rows so that the first row has one marble, the second has 2 marbles, the third has 3, and so on up to 25 rows. How many marbles does the child use in all?