Find the sum to 200 terms of the series 1 + 4 + 6 + 5 + 11 + 6 + ....	Select the correct option:
A) 30,200 B) 29,800 C) 30,400 D) 40,400 E) None of these
Spot the above series is a combination of two APs.   The 1st AP is (1 + 6 + 11 + ....) and the 2nd AP is (4 + 5 + 6 + ...)   Since the terms of the two series alternate   S =(1 + 6 + 11 + .... to 100 terms) + (4 + 5 + 6 + .... to 100 terms)   =&gt; 100[2 x 1 + 99 x 5]/2 + 100[2 x 4 + 99 x 1]/2 ---&gt;(Using the formula for the sum of an AP)   =&gt;50[497 + 107] =50[604] = 30200   Alternatively, we can treat every two consecutive terms as one.   So, we will have a total of 100 terms of the nature:   (1 + 4) + (6 + 5) + (11 + 6).... -&gt; 5, 11, 17,....   Now, a= 5, d=6 and n=100   Hence the sum of the given series is   S= 100/2 x[2 x 5 + 99 x 6]   =&gt; 50[604]   =&gt; 30200   30,200NSWER:30,200
<result>A</result>
Find the sum to 200 terms of the series 1 + 4 + 6 + 5 + 11 + 6 + ....