Project ForgeGeneral Aptitude
Quantitative Aptitude
GATE 2020
Hard
The sum of the first n terms in the sequence 8, 88, 888, 8888, ... is_____.
- A(81/80)(10^n - 1) + (9/8)n
- B(81/80)(10^n - 1) - (9/8)n
- C(80/81)(10^n - 1) + (8/9)n
- (80/81)(10^n - 1) - (8/9)n
Explanation
Each term is 8x(10^k-1)/9 for k=1,2,...,n. Sum = (8/9) x sum_{k=1}^{n}(10^k-1) = (8/9) x [(10(10^n-1))/9 - n] = (80/81)(10^n-1) - (8/9)n.
Source: GATE ME 2020 Session 1 (ME-1) (2020)
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