There are 128 three-digit numbers that are divisible by 7, forming an arithmetic progression (AP).
Explanation
The reference text explicitly states that there are 128 three-digit numbers divisible by 7 which form an AP. This is derived from the following facts:
- The smallest three-digit number divisible by 7 is 105 (7 x 15).
- The largest three-digit number divisible by 7 is 994 (7 x 142).
- Therefore, the three-digit numbers divisible by 7 form an AP: 105, 112, 119, ..., 994.
Additional Insights from the Reference
The reference also provides some helpful properties of arithmetic progressions (AP):
- If each term of an AP is increased, decreased, multiplied, or divided by the same non-zero constant, the resulting sequence will also be in AP.
- In an AP, the sum of terms equidistant from the beginning and end will be constant.
These properties highlight the structured nature of arithmetic progressions and their predictable behavior under certain transformations. While not directly used to calculate the number of terms in the AP of three-digit numbers divisible by 7, they offer a deeper understanding of APs in general.
