Q16. Find the sum of all natural numbers which are less than 500 and also which are multiple of 7. ਉਨਾਂ ਸਾਰੀਆਂ ਪ੍ਰਾਕ੍ਰਿਤਿਕ ਸੰਖਿਆਵਾਂ ਦਾ ਜੋੜ ਪਤਾ ਕਰੋ ਜੋ 500 ਤੋਂ ਘੱਟ ਹੋਣ ਅਤੇ 7 ਨਾਲ ਭਾਗ ਯੋਗ ਹੋਣ । *
16892
17892
18892
19892
Answers
Required Answer :
Option (2) 17892
The sum of all natural numbers which are less than 500 and also which are multiple of 7 = 17892
Solution :
⇒ Arithmetic Progression = 7, 14, 28, ……… 497
we have,
- First term = 7
- last term = 497
⇒ Common difference = t₂ - t₁
⇒ Common difference = 14 - 7
⇒ Common difference = 7
Using formula,
- l = a + (n - 1)d
where,
- l denotes the last term
- a denotes the first term
- n denotes the number of terms
- d denotes the common difference
⇒ 497 = 7 + (n - 1)7
⇒ 497 - 7 = (n - 1)7
⇒ 490 = 7n - 7
⇒ 490 + 7 = 7n
⇒ 497 = 7n
⇒ 497/7 = n
⇒ 71 = n
Number of terms = 71
Using formula,
- Sₙ = n/2[a + l]
⇒ Sum = 71/2 [7 + 497]
⇒ Sum = 71/2 [504]
⇒ Sum = 71/2 × 504
⇒ Sum = 71 × 252
⇒ Sum = 17892
Therefore,
- The sum of all natural numbers which are less than 500 and also which are multiple of 7 = 17892
Given :- Find the sum of all natural numbers which are less than 500 and also which are multiple of 7. ਉਨਾਂ ਸਾਰੀਆਂ ਪ੍ਰਾਕ੍ਰਿਤਿਕ ਸੰਖਿਆਵਾਂ ਦਾ ਜੋੜ ਪਤਾ ਕਰੋ ਜੋ 500 ਤੋਂ ਘੱਟ ਹੋਣ ਅਤੇ 7 ਨਾਲ ਭਾਗ ਯੋਗ ਹੋਣ । *
A) 16892
B) 17892
C) 18892
D) 19892
Solution :-
Number less than 500 and multiples of 7 are :- 7, 14, 21, 28, _______ 497 . since given series is in AP whose first term is 7 and common difference is also 7 .
Let nth term of AP is 497 .
so,
→ a + (n - 1)d = 497
→ 7 + (n - 1)7 = 497
→ 7 + 7n - 7 = 497
→ 7n = 497
→ n = 71
then,
→ Sn = (n/2)[ first term + Last term ]
→ Sn = (71/2)(7 + 497)
→ Sn = (71/2) * 504
→ Sn = 71 * 252
→ Sn = 17892 (B) (Ans.)
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