+0  
 
0
61
1
avatar

Suppose that \(\{a_n\}\)is an arithmetic sequence with 

\(a_1+a_2+ \cdots +a_{100}=100 \quad \text{and} \quad a_{101}+a_{102}+ \cdots + a_{200}=200.\)

 

what is the value of \(a_2 - a_1\)? Express your answer as a common fraction.

Guest Jun 27, 2018
 #1
avatar
0

Sum =N/2*[2F + (N - 1) * D, where N=Number of terms, F=First term, D=Common difference.

First term =101/200, Common difference =1/100, Number of terms =100

Sum =100/2*[(2*101/200) + (100 - 1) * 1/100]

Sum =50 * [(202/200) + (99) * 1/100]

Sum = 50 * [1.01 + 0.99]

Sum =50 *     2

Sum=100 - sum of the 1st. sequence

 

Second sequence = 301/200 =F, Common difference =1/100, Number of terms =100

Sum = 100/2 * [(2*301/200) + (99) * 1/100]

Sum = 50 * [(602/200) + 0.99]

Sum = 50 * [3.01 + 0.99]

Sum = 50 *       4

Sum = 200 - sum of the 2nd. sequence.

So, a(2) - a(1) =(103/200 - 101/200) =1/100

Guest Jun 27, 2018

9 Online Users

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.