NSEJS - Arithmetic Progression

NSEJS - Arithmetic progression

Arithmetic progression

In a Society, the houses are arranged in one line numbering 1 to 49. What is that value of 'x' for which the sum of the numbers of the houses preceding the house number 'x' is equal to the sum of the numbers of the houses following it.

Arithmetic Progression

 The sequence  p₁, p₂ ... and q₁, q₂ … are in arithmetic progressions such that p₁ + q₁ = 50 and p₁₁ − p₁₀ = q₉₉ − q₁₀₀. Find the sum of the first 100 terms of the progression, 

( p₁ + q₁),( p₂ + q₂) …

Arithmetic Progression

1.        Find the average of all 5 digit numbers that leave a remainder of 2 when divided by 7.

Arithmetic Progression

If the sums of the first, p, q, r^th terms of an AP are p, q, r respectively, prove that

    

Arithmetic Progression

In an AP if the 8th term is twice the 13th, show that the 2nd term is twice the 10th term

Arithmetic Progression

If p times the p^th term of an AP is q times the q^th term. Then show that the (p + q)^th term of the AP must be zero.

AP

Find the value of the expression:

(2 + 4 + 6 +.... + 100) + (1 + 3 + 5 + 7 + ...... + 99) ÷ 101

Arithmetic Progression

solution of problems in algebra from Hall

Arithmetic progression ↑↑↑↑

Find the sum of all the 11 terms of an AP whose middle most term is 30.

Arithmetic progression

Find the sum of first 17 terms of an AP whose 4th and 9th terms are –15 and –30 respectively.

Arithmetic Progression

If S_n denotes the sum of first n terms of an AP, prove that

S₁₂ = 3(S₈ –S₄)

Arithmetic Progression

In an AP, if Sn = 3n² + 5n and a_k = 164, find the value of k.

 

Arithmetic progression

Find the sum of the following series up to 11 terms

 

Arithmetic Progession

The first term of an AP is –5 and the last term is 45. If the sum of the terms of the AP is 120, then find the number of terms and the common difference.

Arithmetic Progression

Split 207 into three parts such that these are in AP and the product of the two smaller parts is 4623.

Arithmetic Progression

The angles of a triangle are in AP. The greatest angle is twice the least. Find all the angles of the triangle.

Arithmetic progression

Which term of the AP: 53, 48, 43,... is the first negative term?

Arithmetic progression ↑↑↑↑

How many numbers lie between 10 and 300, which when divided by 4 leave a remainder 3?