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  • Find the value of the sum of the 8th terms of the PRIME integers, where each term is expressed as <img alt="\mathrm{ n^2+4 n-3}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%

Find the value of the sum of the 8th terms of the PRIME integers, where each term is expressed as \mathrm{ n^2+4 n-3}

Option: 1

680


Option: 2

580


Option: 3

380


Option: 4

700


Answers (1)

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Find the value of the sum of the 8th terms of the PRIME integers, where each term is expressed as \mathrm{n^2+4 n-3.}
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To find the sum of the 8th terms of the PRIME integers, where the nth term is expressed as \mathrm{n^2+4 n-3}, we need to substitute the values of n from 1 to 8 into the expression and sum them up.

The sum of the first 8 terms can be calculated as follows:

\mathrm{ \text { Sum }=\left(1^2+4(1)-3\right)+\left(2^2+4(2)-3\right)+\ldots+\left(8^2+4(8)-3\right) }
Simplifying the expression for each term, we have:

\mathrm{ \text { Sum }=(1+4-3)+(4+8-3)+\ldots+(64+32-3) }

Simplifying further, we get:

\mathrm{ \text { Sum }=2+9+\ldots+93 }

To find the sum of an arithmetic series, we can use the formula:

\mathrm{ \text { Sum }=(n / 2)(\text { first term }+ \text { last term }) }
In this case, the first term is 2 , the last term is 93 , and the number of terms is 8 .

Plugging these values into the formula, we get:

\mathrm{ \text { Sum }=(8 / 2)(2+93)=4(95)=380 }
Therefore, the sum of the 8th terms of the PRIME integers, where each term is expressed as

\mathrm{n^2+4 n-3}, is 380 .

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shivangi.bhatnagar

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