The first term of an AP is 100 and the last term of an AP is 2000. The common difference is d=5. how many terms are there and find the sum

Given:- a=100,an=2000,d=5

To find;- nth term and Sn

solution;- since an is given,

we can use; 

Sn=n/2(a+an)

Sn=n/2(100+2000)

Sn=n/2(2100)    ....................(1)            

then;

Sn=n/2(2 a+(n-1)d)

Sn=n/2(2(100)+(n-1)(5))

Sn=n/2(200+5n-5)

Sn=n/2(195+5n)  ....................(2)

from (1) and (2)

2100(n/2)=n/2(195-5n)

2100=195-5n

2100-195=5n

1905=5n

1905/5=n

381=n

n=381

putting the value of n in ........(1)

=2100(n/2)

=2100(381/2)

=2100(190.5)

=4,00,050

Therefore the are 381 terms and the sum is 4,00,050