The sum of the first 7 terms of an A.P. is 63 and the sum of its next 7 terms is 161. Find the 28th term of this A.P.

5

(a)

Find the sum: \(\frac{a - b}{a + b}+\frac{3a - 2b}{a + b}+\frac{5a - 3b}{a + b}+...\) to 11 terms.

5

(a)

In the following A.P., find the missing term: 9, ...., ...., ....., 25

5

(a)

Find the sum of the first 50 odd natural numbers.

5

(a)

If the sum of first p terms of an AP is q and the sum of first q terms is p, then find the sum of first (p + q) terms.

5

(a)

If the sum of first 4 terms of an AP is 40 and that of first 14 terms is 280, find the sum of its n terms.

5

(a)

If the pth terms of an AP is \(\frac{1}{q}\) and the qth term is \(\frac{1}{p}\), show that the sum of pq terms is \(\frac{1}{2}\) (pq + 1).

5

(a)

A thief runs with a uniform speed of 100 m/minute. After one minute, a policeman runs after the thief to catch him. He goes with a speed of 100 m/minute in the first minute and increases his speed by 10 m/minute every succeeding minute. After how many minutes the policeman will catch the thief?

5

(a)

Jaspal Singh repays his total loan of Rs.118000 by paying every month starting with the first instalment of Rs.1000. If he increases the instalment by Rs.100 every month,
(i) What will be paid by him in the 30th instalment?
(ii) What amount of loan does he still have to pay after the 30th instalment?

5

(a)

An AP consists of 37 terms. The sum of the three middle most term is 225 and the sum of the last three is 429. Find the AP.

5

(a)