Question
Download Solution PDF300 থেকে 1000 এর মধ্যে কয়টি সংখ্যা 7 দ্বারা বিভাজ্য?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFপ্রদত্ত শর্ত:
300 এবং 1000 এর মধ্যেকার সংখ্যা যা 7 দ্বারা বিভাজ্য।
ধারণা:
সমান্তর প্রগতি
a n = a + (n - 1)d
গণনা:
প্রথম সংখ্যা যেটি 7 দ্বারা বিভাজ্য (300 - 1000) = 301
একইভাবে: 301, 308, 315, 322...........994
উপরের ক্রমটি একটি সমান্তর প্রগতি তৈরি করে,
যেখানে a = 301, সাধারণ পার্থক্য/d = 308 - 301 = 7 এবং শেষ পদ (an ) = 994
⇒ an = a + (n - 1)d
⇒ 994 = 301 + (n - 1)7
⇒ (994 - 301)/7 = n - 1
⇒ 693/7 + 1 = n
⇒ 99 + 1 = n
⇒ n = 100
∴ 300 এবং 1000 এর মধ্যে 100টি সংখ্যা রয়েছে যেগুলি 7 দ্বারা বিভাজ্য।
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