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  • Calculate the sum of the 10th terms of the PRIME integers, where the nth term is given by <img alt="\mathrm{3 n^2+2 n-1}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7B3%20n%5E2&

Calculate the sum of the 10th terms of the PRIME integers, where the nth term is given by \mathrm{3 n^2+2 n-1}

Option: 1

1020


Option: 2

1856


Option: 3

1615


Option: 4

1444


Answers (1)

To calculate the sum of the 10th terms of the sequence generated by the expression \mathrm{3 n^2+2 n-1}. we need to substitute the values of \mathrm{n} from 1 to 10 into the expression and sum them up.
The 10 th term is given by substituting \mathrm{n=10} into the expression:

\mathrm{ \begin{aligned} & 10^{\text {th }} \text { term }=3(10)^2+2(10)-1 \\\\ & =3(100)+20-1 \\\\ & =300+20-1 \\\\ & =319 \end{aligned} }

To find the sum of the first 10 terms, we can use the formula for the sum of an arithmetic series:

\mathrm{ \begin{aligned} & \text { Sum }=(\mathrm{n} / 2)(\text { first term }+ \text { last term }) \\\\ & =(10 / 2)\left(1^{\text {st }} \text { term }+10^{\text {th }} \text { term }\right) \end{aligned} }

The first term is obtained by substituting \mathrm{ n=1} into the expression:

\mathrm{ \begin{aligned} & 1^{\text {st }} \text { term }=3(1)^2+2(1)-1 \\\\ & =3(1)+2(1)-1 \\\\ & =3+2-1=4 \end{aligned} }

 

\mathrm{ \begin{aligned} & \text { Sum }=(10 / 2)(4+319) \\\\ & =5(323) \\\\ & =1615 \end{aligned} }

Therefore, the sum of the 10 th terms of the sequence generated by \mathrm{3 n^2+2 n-1} is 1615 .

Posted by

Sumit Saini

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