GATE 2020 MT – Question 8

General Aptitude · Quantitative Aptitude: Algebra, Geometry and Mensuration · 2 marks · Multiple choice

Find the sum of the first n terms in the sequence 8, 88, 888, 8888, ….

$\frac{81}{80}(10^n-1)+\frac98n$
$\frac{81}{80}(10^n-1)-\frac98n$
$\frac{80}{81}(10^n-1)+\frac89n$
$\frac{80}{81}(10^n-1)-\frac89n$

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Show answer and explanation

Correct answer: (D) $\frac{80}{81}(10^n-1)-\frac89n$

Explanation

Term k is $8(10^k-1)/9$. Summing gives $S_n=(8/9)[10(10^n-1)/9-n]=80(10^n-1)/81-8n/9$. The geometric series starts at 10, which accounts for the extra factor 10. **Answer: D.**

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