Tamil Nadu Board Solutions for Chapter: Numbers And Sequences, Exercise 34: Exercise 2.9

Find the sum of the following series :

$6^2+7^2+8^2+\dots +{21}^2$

If $1+2+3+\dots +k=325$, then find $1^3+2^3+3^3+\dots \dots \dots \dots +k^3$.

If $1^3+2^3+3^3+\dots +k^3=44100$, then find $1+2+3+\dots +k$.

How many terms of the series $1^3+2^3+3^3+\dots$ should be taken to get the sum $14400$ ?

The sum of the squares of the first n natural numbers is $285,$ while the sum of their cubes is $2025$ Find the value of n

Rekha has $15$ square colour papers of sizes $10\mathrm{cm},11\mathrm{cm},12\mathrm{cm},\dots ,24\mathrm{cm}$. If the area can be decorated with these colour papers is $k {\mathrm{cm}}^2$, then find the value of $k$.

Find the sum of the series $\left(2^3-1\right)+\left(4^3-3^3\right)+\left(6^3-{15}^3\right)+\dots$ to $n$ terms.

Find the sum of the series $\left(2^3-1\right)+\left(4^3-3^3\right)+\left(6^3-5^3\right)+\dots$ to $8$ terms.