Question

In the sequence 1, 7, 13, 19, . . . , each number is 6 more than the number before it. In the sequence 1, 9, 17, 25, . . . , each number is 8 more than the number before it. The two sequences have infinitely many numbers in common. Find the sum of the first three common numbers.

Answer 1

Answer:first three common numbers are

25, 73 and 97

And their sum= 195.

Explanation:

1, 7, 13, 19, . . adding 6 to the terms in this first sequence gives the first 17 terms as

1,7,13,19,25,31,37,43,49,55,61,67,73,79,85,91,97 and

In the second sequence the first 17 terms with the addition of 8 are

1,9,17,25,33,41,49,57,65,73,81,89,97,105, 113,121,129,137

From the above, we can see common terms so far from the two sequence as

25, 73 and 97

Adding them gives a total of 195.