In a sequence, each term is obtained by adding 6 to the preceding one. If the sum of the first 10 terms is equal to 100, what is the result of the addition of the first 30 terms?
Choose the correct choice from the following:
A) 2100 B) 2170 C) 2200 D) 2250 E) 2400
a is first term and d = 6 since the preceding number is always greater than the previous one..   Now 10th term is a+9(6).   Sum of n terms is n/2(first term + last term)and here we have to get sum of 10 terms , we get 10/2 ( a + a+54) = 100 ( given sum of 10 terms is 100)   =&gt; 5(2a+54) = 100   =&gt; 2a+54 = 20   =&gt; a = -17   Now to get sum of first 30 terms , we need to get 30th term value i.e. -17+29(6) = 157.   Sum of first 30 terms = 30/2( -17 + 157) = 2100.   Hence option 2100 is correct answer..
<result>A</result>
In a sequence, each term is obtained by adding 6 to the preceding one. If the sum of the first 10 terms is equal to 100, what is the result of the addition of the first 30 terms?