whole number operations sum

Question: Find four numbers in AP whose sum is 26. Sum of the products of the extremes and the middle terms is 62. Answer: Let (a - 3d), (a - d), (a + d), (a + 3d) be the four numbers in AP The numbers are ..

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..

Let us consider the marks obtained by four students in Physics, Chemistry and Biology for the first unit test. We have represented the data in rows and columns. (i) Rows show the marks obtained by each student. (ii) The columns show the marks in Physics, Chemistry, Biology obtained by each student...

Let S n = 1+2+3+4+...+n This series is an A.P. Here a=1, d=1, l = t n = n 2. To find the sum to squares of first n natural numbers. or..

Step 1: The factor pairs of the last term are (7,2), (14,1), (-1,-14). Step 2: The pair of factors whose sum is equal to -15, the co- efficient of the middle term is (-1,-14). Step 3: Rewrite the expression using these factors Step 4: Group the terms and factorise. ..

For n N, in the expansion of (a + b) n , we observe that: the number of terms is n+1 the exponent of 'a' decreases from n to 0 the exponent of 'b' increases from 0 to n the sum of exponents of 'a' and 'b' in any term is n. the coefficient of any term is n C k ..

Summary - (i) Let X be a set of numbers and f : N n X be a function, then the ordered set {f(1), f(2),...., f(n)} is called a finite sequence in X. (ii) Let X be a set of numbers and f : N X be a function, then the ordered set {f(1), f(2),....} is called an infinite sequence in ..

: These can be inserted between a and b. b. To find the sum of n arithmetic means between the two given quantities: Let the two quantities (numbers) be a and b. The required sum = A 1 + A 2 + A 3 + ---- + A..

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 the numbers is equal to the coefficient of the mid..

Step 1: Factor pairs of the last term are (-7,+3), (21,-1), (+7,-3), (-21,+1). Step 2: The pair of factors whose sum is equal to the co-efficient of the middle term is (+7,-3). Step3: Rewrite the expression using these factors as w 2 + 7w - 3w -21. Step 4: Group the terms and factorise...