Consider the arithmetic progression 3,7,11,… and let Aₙ denote the sum of the first n terms of this progression. Then the value of (1/25)∑(n=1 to 25)Aₙ is
Question:
Consider the arithmetic progression 3,7,11,… and let Aₙ denote the sum of the first n terms of this progression. Then the value of (1/25)∑(n=1 to 25)Aₙ is
Consider the arithmetic progression 3,7,11,… and let Aₙ denote the sum of the first n terms of this progression. Then the value of (1/25)∑(n=1 to 25)Aₙ is
Options
Answer: (3) 455
Explanation:
AP with a=3, d=4. Aₙ = n/2[2×3+(n-1)×4] = n(2n+1). ∑Aₙ = ∑n(2n+1) = 2∑n² + ∑n = 2×25×26×51/6 + 25×26/2 = 11375. Answer = 11375/25 = 455.
Explanation:
AP with a=3, d=4. Aₙ = n/2[2×3+(n-1)×4] = n(2n+1). ∑Aₙ = ∑n(2n+1) = 2∑n² + ∑n = 2×25×26×51/6 + 25×26/2 = 11375. Answer = 11375/25 = 455.
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