brodidit for students
تسلسل اور سلسلے
نیٹ · ریاضی · 5 سوالات
نام: ____________________ تاریخ: ____________
What is the sum of the first 6 terms of the geometric series 3 + 6 + 12 + ...?
- A 381
- B 96
- C 192
- D 189
What is the 20th term of the sequence 2, 5, 8, 11, ...?
- A 62
- B 60
- C 59
- D 57
What is the arithmetic mean between 4 and 16?
- A 12
- B 10
- C 20
- D 8
What is the geometric mean between 4 and 16?
- A 8
- B 64
- C 6
- D 10
What is the sum of the first 10 odd natural numbers, 1 + 3 + 5 + ...?
- A 110
- B 55
- C 90
- D 100
جوابی کلید
1. D, 2. C, 3. B, 4. A, 5. D
S₆ = a(r⁶ - 1) / (r - 1) = 3 x 63 = 189.
The nth term is 2 + (n - 1) x 3 = 3n - 1. For n = 20 it is 59.
The arithmetic mean of two numbers is half their sum: (4 + 16) / 2 = 10.
The geometric mean is the square root of the product: sqrt(4 x 16) = sqrt(64) = 8.
The sum of the first n odd numbers is n², so for n = 10 the sum is 100.