Arithmetic Progression : Arithmetic Progression
Slide2 : Sequence: A list of numbers having specific relation between the consecutive terms is generally called a sequence.
e.g. 1, 3, 5, 7,……… (next term to a term is obtained by adding 2 with it)
& 2, 6, 18, 54,…….( next term to a term is obtained by multiplying 3 with it)
Slide3 : Arithmetic Progression: If various terms of a sequence are formed by adding a fixed number to the previous term or the difference between two successive terms is a fixed number, then the sequence is called AP.
e.g. 2, 4, 6, 8, ……… the sequence of even numbers is an example of AP
Slide4 : Common Difference –
The fixed number which is obtained by subtracting any term of AP from its previous term.
If we take
first term of an AP as a
and Common Difference as d,
Then,
nth term of that AP will be
t(n) = a + (n-1) d
Slide5 : The sum of n terms, we find as,
Sum = n X [(first term + last term) / 2]
Now last term will be = a + (n-1) d
Therefore,
Sum =n X [{a + a + (n-1) d } /2 ]
= n/2 [ 2a + (n+1)d]
Slide6 : The difference between two terms of an AP can be formulated as below:-
nth term – kth term
= t(n) – t(k)
= {a + (n-1)d} – { a + (k-1) d }
= a + nd – d – a – kd + d = nd – kd
Hence,
t(n) – t(k) = (n – k) d
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