If the 10^th~ term of an A.P. is 120 and its 20^th~ term is 110, then the sum of its first 200 terms is

(d) : Given, T_10=120=a+9 d and T_20=110=a+19 d (i) and (ii), we have a=1200, d=1200 S_200=2002[2200+199200]=2012=100 12

If the 10^{{th}{~}} term of an A.P. is \frac{1}{20} and its 20^{{th}{~}} term is \frac{1}{10}, then the sum of its first 200 terms is: Sequence & Series (Mathematics)

(d) : Given,

T_{10}=\frac{1}{20}=a+9 d

and

T_{20}=\frac{1}{10}=a+19 d

\nSolving (i) and (ii), we have

a=\frac{1}{200}, d=\frac{1}{200}

\n\therefore S_{200}=\frac{200}{2}\left[\frac{2}{200}+\frac{199}{200}\right]=\frac{201}{2}=100 \frac{1}{2}\n