If 9 times the  9th term of an AP is equal to 13 times the 13th term, then find the 22nd term of the AP.

2

(a)

The p th term of an AP is a and q th term is b. Prove that sum of its (p+q) th term is \(\frac { p+q }{ 2 } \left[ a+b+\frac { a-b }{ p-q } \right] .\)

2

(a)

(i) If a, b, c, d are four distinct positive quantities in AP, then show that bc > ad.

2

(a)

(ii) If a, b, c, d are four distinct positive quantities in GP then show that a + d > b + c.

2

(a)

At the end of each yearthe value of a certain machine has depreciated by 20% of its value at the begining of that year. If its initial value was Rs.1250, then find the value at the end of 5 yrs.

2

(a)