Arithmetical progression(AP)

Definition: In the sequencial series, if commen difference between any two successive terms is same the sequence is called in AP.

Ex: 2,4,6,8,10...

here, first term=t1=a=2

    second term=t2=4

    third term=t3=6

similarly, t4=8,t5=10  so on

Hence common difference(d)=t2-t1=t3-t2=t4-t3=t5-t4

                                         =4-2=6-4=8-6=10-8

                                          =2

1)Formula to find the nth term(ex; 5th term(t5), 8th term(t8), 17th term(t17) etc--

Tn=a+(n-1)d

here, a=first term,n=number of terms,d=common difference

In the above example to find the 25th term(t25)

here,a=2,d=2,n=25

∴ T25=2+(25-1)2

        =2+(24*2)

        =2+48=50

∴ T25=50

2)Formula to find the sum of n terms is given by:-

Sn=n/2⌈ 2a+(n-1)d⌉

Now for the above example:

1)In the above example to find the sum of 100 terms

a=2,d=2 and n=100

S100=100/2⌈ 2*2+(100-1)2⌉

        =50 ⌈ 4+(99)2⌉

         =50⌈ 4+198⌉

          =50(202)

           =10100