Arithmetic Progression (A.P.)

A manufacturer reckons that the value of a machine, which costs him Rs 15625, will depreciate each year by 20%. Find the estimated value at the end of 5 years.

If a, b, c is in A.P., then show that:

bc − a², ca − b², ab − c² are in A.P.

Find the sum of all integers between 100 and 550, which are divisible by 9.

if `(a^n + b^n)/(a^(n-1) + b^(n-1))` is the A.M. between a and b, then find the value of n.

If 10 times the 10th term of an A.P. is equal to 15 times the 15th term, show that 25th term of the A.P. is zero.

How many terms of the A.P. −6, \[- \frac{11}{2}\], −5, ... are needed to give the sum −25?

If S₁ be the sum of (2n + 1) terms of an A.P. and S₂ be the sum of its odd terms, then prove that: S₁ : S₂ = (2n + 1) : (n + 1).

The sum of the first four terms of an A.P. is 56. The sum of the last four terms is 112. If its first term is 11, then find the number of terms.