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  • Calculate the sum of the 10th terms of the PRIME integers, where the nth term is expressed as <img alt="\mathrm{2 n^3-n^2+3 n}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7

Calculate the sum of the 10th terms of the PRIME integers, where the nth term is expressed as \mathrm{2 n^3-n^2+3 n}

Option: 1

9670


Option: 2

3709


Option: 3

4100


Option: 4

5278


Answers (1)

best_answer

Calculate the sum of the 10th terms of the PRIME integers, where the nth term is expressed as \mathrm{2 n^3-n^2+3 n}

To find the sum of the 10th terms of the PRIME integers, where the nth term is expressed as \mathrm{2 n^3-n^2+3 n}, we need to substitute the values of $\mathrm{n}$ from 1 to 10 into the expression and sum them up.

The sum of the first 10 terms can be calculated as follows:

\mathrm{ \text { Sum }=\left(2(1)^3-(1)^2+3(1)\right)+\left(2(2)^3-(2)^2+3(2)\right)+\ldots+\left(2(10)^3-(10)^2+3(10)\right) }

Simplifying the expression for each term, we have:

\mathrm{ \text { Sum }=(2-1+3)+(16-4+6)+\ldots+(2000-100+30) }

Simplifying further, we get:

\mathrm{ \text { Sum }=4+18+\ldots+1930 }

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 4 , the last term is 1930 , and the number of terms is 10 . Plugging these values into the formula, we get:

\mathrm{ \text { Sum }=(10 / 2)(4+1930)=5(1934)=9670 }

Therefore, the sum of the 10th terms of the PRIME integers, where the nth term is expressed as

\mathrm{2 n^3-n^2+3 n, \, \, is \, \, 9670 .}

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