Arithmetic Progression is one the most important and scoring
Topics in class tenth mathematics. In this article, we will learn the basic
concepts of arithmetic progression.
An Arithmetic progression can be defined as
a sequence of numbers in which the consecutive terms (beginning with the second
term) are formed by adding a constant quantity with the preceding term.
Examples of arithmetic expression are –
- Natural number – 1,2,3,4,5…. With 1 as first
term as well as the constant quantity. - 2,4,6,8,10…. It is an AP with 2 as first term as
well as the constant quantity. - 4,4,4,4,4,4…. It is an AP with 4 as first term
and 0 as the constant quantity. - A taxi charges Rs 16 for first km and Rs 10 each
additional km. Fare would be 16, 26, 36…. - Price of a commodity is Rs 80. Each year its
price decreases by Rs 10.
Resulting AP would be 80, 70, 60, 50… where
80 is the first term and -10 is the constant quantity.
Finite Arithmetic Progression can be defined as the
AP with finite number of terms. For example, AP – 2,4,6,8,10 has 5 terms.
Infinite Arithmetic Progression can be defined as the
AP with infinite number of terms. For example, AP – 3,6,9,12…. has infinite
number of terms.
First term of an Arithmetic Progression is denoted by
symbol ‘a’. Common Difference(constant quantity) is denoted by symbol
‘d’.
General form of AP is - a, a+d, a+2d, a+3d….
To determine the value of a term at a certain position in
the AP, we have the formula for nth term of an AP.
nth term of
AP, an = a + (n-1) d
Sum of first n terms, Sn, can be determined by
Sn
= n/2 [2a + (n-1) d]
Also, if the nth of the last term, l, is already known then
sum of first n terms would be
Sn
= n/2 [a + l]
Arithmetic mean is the quantity obtained by summing
two or more numbers or variables and then dividing by the number of numbers or
variables. For example, if a,b,c are in AP, then b = [a+c]/2 and b would be
called as arithmetic mean of a and c.https://youtu.be/qfA7RzrEkho
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