Find the sum of all natural numbers between 250 and 1000 which are exactly divisible by 7
Answers
Answered by
1
Answer:
66661
Step-by-step explanation:
We need to find the sum of all natural numbers between 250 and 1000 which are divisible by 7
It is an arithmetic progression as each next term is 7 more then previous one.
- Common difference is obviously 7
Lets find the first and last terms and number of terms
- To find the first term lets divide 250 by 7: 250/7= 35 with reminder, so the first term is (35+1)*7= 36*7=252
- To find the last term lets divide 1000 by 7: 1000/7= 142 with reminder, so the last term is 142*7=994
- Number of terms= 142-36+1=107 (note: +1 is to include both terms)
Now let's find the required sum:
- As per AP sum of n terms formula: Sₙ=n/2*(a₁+aₙ)
- So, S₁₄₂=107/2*(252+994)=66661
The answer is 66661
Similar questions