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A student taking a test consisting of 10 questions is told that each question after the first question is worth 2 marks more than the preceding questions. If third question of the test worth 5 marks , what is the maximum score that the student can obtain by attempting 8 questions.

The answer is 96 marks. I want explanation.

The maximum marks can be scored by obtaining full marks from 3^{rd} to 10^{th} questions.

Here,

*a*= 5,*d*= 2,*n*= 8[Marks to 3

$\mathrm{So},{\mathrm{S}}_{8}=\frac{\mathrm{n}}{2}\left[2\mathrm{a}+(\mathrm{n}-1)\mathrm{d}\right]\phantom{\rule{0ex}{0ex}}=\frac{8}{2}\left[\left(2\times 5\right)+\left(8-1\right)\left(2\right)\right]\phantom{\rule{0ex}{0ex}}=4\left[10+14\right]\phantom{\rule{0ex}{0ex}}=96$

So, maximum mark that the student can obtain is 96.

Regards

^{rd}question = 5, 10^{th}question is 8^{th}term when first term is 3^{rd}question]$\mathrm{So},{\mathrm{S}}_{8}=\frac{\mathrm{n}}{2}\left[2\mathrm{a}+(\mathrm{n}-1)\mathrm{d}\right]\phantom{\rule{0ex}{0ex}}=\frac{8}{2}\left[\left(2\times 5\right)+\left(8-1\right)\left(2\right)\right]\phantom{\rule{0ex}{0ex}}=4\left[10+14\right]\phantom{\rule{0ex}{0ex}}=96$

So, maximum mark that the student can obtain is 96.

Regards

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