# The sum of all the terms common to the arithmetic progressions 1, 3, 5, ....., 1991 and 1, 6, 11, ......., 1991, is? (1) 199100 (2) 199200 (3) 199300 (4) 200196

##### 1 Answer

Dec 18, 2016

(2)

#### Explanation:

Given:

#1, 3, 5,...,1991#

#1, 6, 11,...,1991#

Note that the common difference of the first sequence is

Since these have no common factor greater than

#1, 11, 21, 31,..., 1991#

This sequence has

#1/2 * (1+1991) = 1992/2#

So the sum is:

#200*1992/2 = 199200#