Question

What is the reminder on dividing the terms of the arithmetic sequence 100,107,114,.....by 7

Answer 1

Answer:

2

Step-by-step explanation:

First off, notice that the arithmetic sequence has a difference of 7 between consequtive terms. As the remainder of $7n$ when dividing by 7 is 0 for all $n \in \mathbb{Z}$ then all of the terms in the sequence have the same remainder when dividing by 7. Then finding the remainder of 100 when dividing by 7 is enough to answer the question. We then notice that $98 = 7 \times 14$ is the largest multiple of 7 that is less than 100. As 100-98 = 2, then the remainder of 100 when divided by 7 is 2. Consequently the remainder of the terms of the arithemtic sequence when divided by 7 is 2.