the sum of a number and 5 less than that number is three times the same number. find the number.

Question: Four numbers are in AP. Sum of the first three is 21 and sum of last three is 30. Find the numbers. Answer: Let the numbers a - 3d, a - d, a + d, a + 3d be in AP. ..

Question: Show that the sum of the cubes of any number of consecutive integers is divisible by the sum of those integers. Answer: Let the consecutive integers be (n + 1), (n + 2), (n + 3),....,(n + m) Sum of the cubes of integers = S 1 ..

Considering the same example. x - 2------------------ (5x - 7) (x - 1) partial fraction can be written as: x - 2 A B ----------------- = ---------- + --------- (5x - 7)(x - 1) (5x - 7) (x - 1) Multiply the denominators on ..

Example 2.Subtract the fraction ½ by 1/10 Solution : Step 1. The bottom numbers are different. We need to make them the same. We can multiply the top and bottom of ½ by 5 like this: And now the bottom numbers (the denominators) are the same: Now ..

The Greek letter S (read as sigma) denotes the sum. When written before the n t h term of series, implies, the sum of all terms obtained by giving to n the different values 1,2,3n. Thu..

skew-symmetric for every square matrix A. That is any square matrix is expressible as the sum of a symmetric matrix and a skew-symmetric matrix. 5. A matrix which is both symmetric and skew symmetric is a zero matr..

Find 'a.c ', the product of the coefficient of x 2 and the last term. Find all the factor pairs of 12. (1,12), (3,4), (2,6) are the factor pairs of 12. The factor pair (3,4) is such that 3 + 4 = 7and 3 x 4 = 12 i.e, sum of ..

To manipulate compound fractions, just convert them to simple fractions . Example : Convert to a simple fraction. Answer. can be written . Write 3 as the fraction . Now can be written and..

Question: If S n = 2n 2 + 3n denote the sum of a progression, prove that it is an AP. Find (2n) t h term. Answer: d is independent of n. The progression is an AP. ..

Question: If S 1 , S 2 , S 3 ,....., S n are the sums of infinite GP's whose first Answer: This is an AP with a = 2, d = 1 and n = n ..