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
Written on Aug. 23, 2018, 11:18 p.m.