Question

The arithmetic sequences 1, 5, 9, 13,... and 1, 8, 15, 22,... have infinitely many terms in common. Calculate the sum of the first three common terms.

Answer 1

87

Explanation:

The first sequence:

1, 5, 9, 13, 17, 21, 25, 29, 33, 37, 41, 45, 49, 53, 57, 61...

The second sequence:

1, 8, 15, 22, 29, 36, 43, 50, 57, 63...

The first three common terms are 1, 29, 57.

The sum of the first three common terms:

1 + 29 + 57

= 87

Answer 2

87

Explanation:

Sequence 1 has common difference of 4 and sequence 2 has 7

The first terms are common

We need a new sequence with common difference of:

• LCM(4,7)= 4*7=28

So the next common term is 1+28= 29 and the following one is 29+28= 57

Sum of 3 terms:

• 1+29+57= 87