Page 7 - Arithmetic

So, 21 = (5 × 4) + 1
Worked Example 5
When 8746 is divided by a number, the quotient is 78, and the remainder is 10. What is the divisor?
Solution:
Dividend = (Quotient × Divisor) + Remainder 8746 = (78 × Divisor) + 10
8736 = 78 × Divisor
Divisor = 112
Progression
When numbers are arranged in succession, and in a definite order as per a rule, the series is called progression.
For example,
1, 2, 3, 4, 5....
Here the series is arranged in succession and the difference between immediate two numbers is 1.
Arithmetic Progression
It’s a series of numbers such that the difference between two immediate or consecutive terms is a constant. The constant term is called the common difference and is denoted by ‘d’. Also, the first term of A.P. is denoted by ‘a’.
For example,
1, 3, 5, 7, 9....
Here, the difference between two consecutive terms is 2. 3-1 = 5-3 = 7-5 = 2.
So, a = 1 and d = 2
REMEMBER:
An A.P. series is denoted by
a, a + d, a + 2d, a + 3d, a + 4d...... The nth term of any A.P. is given by: Tn =a+(n–1)d
Sum of the terms of AP = Sn = 𝑛 [2a + (n – 1)d] = 𝑛 [first term + last term] 22
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Arithmetic Concept