Free Printable Sigma Notation

1.

Given that $\sum_{r=1}^nr^2=\frac{n}{6}\left(n+1\right)\left(2n+1\right)$ , find $\sum_{a=1}^na^2$

a)

$\frac{a}{6}\left(a+1\right)\left(2a+1\right)$

b)

$\frac{n}{6}\left(n+1\right)\left(2n+1\right)$

c)

$na^2$

d)

$\frac{r}{6}\left(r+1\right)\left(2r+1\right)$

2.

Given that $\sum_{r=1}^nr^2=\frac{n}{6}\left(n+1\right)\left(2n+1\right)$ , find $\sum_{r=1}^na^2$

a)

$\frac{a}{6}\left(a+1\right)\left(2a+1\right)$

b)

$\frac{n}{6}\left(n+1\right)\left(2n+1\right)$

c)

$na^2$

d)

$\frac{r}{6}\left(r+1\right)\left(2r+1\right)$

3.

Given that $\sum_{r=1}^nr^2=\frac{n}{6}\left(n+1\right)\left(2n+1\right)$ , find $\sum_{r=3}^{10}a^2$

a)

$204$

b)

$385$

c)

$8a^2$

d)

$7a^2$

4.

Given that $\sum_{r=1}^nr^2=\frac{n}{6}\left(n+1\right)\left(2n+1\right)$ , find $\sum_{r=1}^{10}r^2$

a)

$10r^2$

b)

$385$

c)

$9r^2$

d)

$\frac{r}{6}\left(r+1\right)\left(2r+1\right)$

5.

Given that $\sum_{r=1}^nr^2=\frac{n}{6}\left(n+1\right)\left(2n+1\right)$ , find $\sum_{a=1}^{n+1}a^2$

a)

$na^2$

b)

$\left(n+1\right)^2$

c)

$\frac{a+1}{6}\left(a+2\right)\left(2a+3\right)$

d)

$\frac{n+1}{6}\left(n+2\right)\left(2n+3\right)$

6.

Given that $\sum_{r=1}^nr^2=\frac{n}{6}\left(n+1\right)\left(2n+1\right)$ , find $\sum_{r=11}^{n+1}r^2$

a)

$\left(n-10\right)r^2$

b)

$\frac{n+1}{6}\left(n+2\right)\left(2n+3\right)-506$

c)

$\frac{a+1}{6}\left(a+2\right)\left(2a+3\right)-385$

d)

$\frac{n+1}{6}\left(n+2\right)\left(2n+3\right)-385$

7.

Given that $\sum_{r=1}^nr^2=\frac{n}{6}\left(n+1\right)\left(2n+1\right)$ , find $\sum_{r=8}^{n-2}\left(r+3\right)^2$

a)

$\left(n-3\right)^2$

b)

$\left(n+3\right)^2$

c)

$\sum_{r=11}^{n-2}r^2$

d)

$\sum_{r=11}^{n+1}r^2$

8.

Given that $\sum_{r=1}^nr^2=\frac{n}{6}\left(n+1\right)\left(2n+1\right)$ , find $\sum_{r=8}^{n-2}\left(2r+3\right)^2$

a)

$\left[2\left(n-9\right)+3\right]^2$

b)

$4\sum_{r=8}^{n-2}r^2+9\left(n-9\right)$

c)

$\sum_{r=19}^{2n-1}r^2$

d)

$4\sum_{r=8}^{n-2}r^2+12\sum_{r=8}^{n-2}r+9\left(n-9\right)$

9.

Given that $\sum_{r=1}^nr^2=\frac{n}{6}\left(n+1\right)\left(2n+1\right)$ and $\sum_{r=1}^nr=\frac{n}{2}\left(n+1\right)$ , find $\sum_{r=1}^n\left(r^2+3n\right)$

a)

$\frac{n}{6}\left(n+1\right)\left(2n+1\right)+3n^2$

b)

$\frac{n}{6}\left(n+1\right)\left(2n+1\right)+3n$

c)

$\frac{n}{6}\left(n+1\right)\left(2n+1\right)+\frac{3n}{2}\left(n+1\right)$

d)

$n^2+3n$

10.

Given that $\sum_{r=1}^nr^2=\frac{n}{6}\left(n+1\right)\left(2n+1\right)$ and $\sum_{r=1}^nr=\frac{n}{2}\left(n+1\right)$ , find $\sum_{r=1}^n\left(4r^2-3r+6\right)$

a)

$\frac{2r}{3}\left(r+1\right)\left(2r+1\right)-\frac{3r\left(r+1\right)}{2}+6r$

b)

$\frac{2n}{3}\left(n+1\right)\left(2n+1\right)-\frac{3n\left(n+1\right)}{2}+6$

c)

$\frac{2n}{3}\left(n+1\right)\left(2n+1\right)-3n+6$

d)

$\frac{2n}{3}\left(n+1\right)\left(2n+1\right)-\frac{3n\left(n+1\right)}{2}+6n$

Sigma Notation

Total questions: 10

Worksheet time: 10mins

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