English Medium Class 10 - CBSE Important Questions

If S_n¹ denotes the sum of first n terms of an A.P., prove that S₁₂ = 3(S₈ − S₄).

If the sum of the first n terms of an A.P. is `1/2`(3n² +7n), then find its n^th term. Hence write its 20^th term.

The first and the last terms of an AP are 7 and 49 respectively. If sum of all its terms is 420, find its common difference.

If S_n denotes the sum of first n terms of an A.P., prove that S₃₀ = 3[S₂₀ − S₁₀]

The first and the last terms of an AP are 8 and 65 respectively. If the sum of all its terms is 730, find its common difference.

Find the sum of first 20 terms of the following A.P. : 1, 4, 7, 10, ........

The ratio of the sums of m and n terms of an A.P. is m² : n². Show that the ratio of the m^th and n^th terms is (2m – 1) : (2n – 1)

How many multiples of 4 lie between 10 and 250?

How many terms of the AP. 9, 17, 25 … must be taken to give a sum of 636?

Find the sum of first 51 terms of an AP whose second and third terms are 14 and 18 respectively.

The sum of the third and the seventh terms of an AP is 6 and their product is 8. Find the sum of first sixteen terms of the AP.

If the sum of first m terms of an A.P. is the same as the sum of its first n terms, show that the sum of its first (m + n) terms is zero

If the pth term of an A. P. is `1/q` and qth term is `1/p`, prove that the sum of first pq terms of the A. P. is `((pq+1)/2)`.

Which term of the progression 20, 19`1/4`,18`1/2`,17`3/4`, ... is the first negative term?

Which term of the A.P. `20, 19 1/4, 18 1/2, 17 3/4,` ..... is the first negative term?

Find the common difference of an AP whose first term is 5 and the sum of its first four terms is half the sum of the next four terms.

The 24^th term of an AP is twice its 10^th term. Show that its 72^nd term is 4 times its 15^th term. 

How many two-digit number are divisible by 6?

How many two-digits numbers are divisible by 3?

How many terms of the A.P. 21, 18, 15, … must be added to get the sum 0?