Class X : HOTS Question Answers: Math Unit - 5 (Arithmetic Progression)

ARITHMETIC PROGRESSIONS

1. The fourth term of an AP is 0. Prove that its 25th term is triple its 11th term

2. Find the 20th term from the end of the AP 3, 8, 13……..253

3. If the pth, qth & rth term of an AP is x, y and z respectively,
   show that x(q-r) + y(r-p) + z(p-q) = 0

4. Find the sum of first 40 positive integers divisible by 6 also find the sum of first 20 positive integers divisible by 5 or 6.

5. A man arranges to pay a debt of Rs.3600 in 40 monthly installments which are in a AP. When 30 installments are paid he dies leaving one third of the debt unpaid. Find the value of the first instalment

6. Find the sum of all 3 digit numbers which leave remainder 3 when divided by 5.

7. Find the value of x if 2x + 1, x2 + x +1, 3x2 - 3x +3 are consecutive terms of an AP

8. Raghav buys a shop for Rs.1,20,000.He pays half the balance of the amount in cash and agrees to pay the balance in 12 annual installments of Rs.5000 each. If the rate of interest is 12% and he pays with the installment the interest due for the unpaid amount. Find the total cost of the shop.

9. Prove that am + n + am - n =2am

10. If the roots of the equation (b-c)x2 +(c-a) x +(a-b) = 0 are equal show that a, b, c are in AP.&