Theory question 102
Sequences and SeriesFind the sum of all natural numbers between 403 and 603 which are divisible by 7.
Show the model answer
Model answer
First multiple of 7 above 403 is 406 (7 × 58); last below 603 is 602 (7 × 86).
Number of terms n = 86 − 58 + 1 = 29.
Sum = 29/2 × (406 + 602) = 29 × 504 = 14 616.
Explanation
The multiples form an A.P. with common difference 7.