UPSC NDA Math Model Paper 2

The multiples of 7 form an Arithmetic Progression with common difference 7.
200 ÷ 7 = 28.57... and 400 ÷ 7 = 57.14...
∴ The first multiple of 7 after 200 will be 7 × 29 = 203 and the last multiple of 7 before 400 will be 7 × 57 = 399.
Let's say that 399 is the n‌th term of the AP.
∴ 399 = 203 + (n - 1)7
⇒ 7n - 7 = 196
⇒ 7n = 203
⇒ n = 29
This means, there are 29 terms from 203 to 399 with a common difference of 7. The sum of these numbers will be:
S29=(

First Term + Last Term

2

)×29
⇒S29=(

203+399

2

)×29
⇒S29=(

602

2

)×29
⇒S29=301×29
⇒S29=8729