Kerala Board Solutions for Chapter: Arithmetic Sequences, Exercise 7: Exercise 7

Calculate the sum of the following arithmetic sequence.

$51+52+53+.......+70$

Calculate the sum of the following arithmetic sequence.

$1\frac{1}{2}+2\frac{1}{2}+......+12\frac{1}{2}$

Calculate the sum of the following arithmetic sequence.

$\frac{1}{2}+1+1\frac{1}{2}+2+2\frac{1}{2}+......+12\frac{1}{2}$

Prove that the sum of any number of terms of the arithmetic sequence $16, 24, 32,\dots ..$.. starting from the first, added to $9$ gives a perfect square

$$\begin{gathered} 1 \\ 2 3 \\ 4 5 6 \\ 7 8 9 10 \\ ...................... \\ ............................ \end{gathered}$$

Write the next two lines of the pattern above.

$$\begin{gathered} 1 \\ 2 3 \\ 4 5 6 \\ 7 8 9 10 \\ ...................... \\ ............................ \end{gathered}$$

Write the first and the last numbers of the ${10}^{\mathrm{th}}$ line.

$$\begin{gathered} 1 \\ 2 3 \\ 4 5 6 \\ 7 8 9 10 \\ ...................... \\ ............................ \end{gathered}$$

Find the sum of all the numbers in the first ten lines.

$$\begin{gathered} 4 \\ 7 10 \\ 13 16 19 \\ 22 25 28 31 \\ .................... \\ ...................... \end{gathered}$$

Write the next two lines of the pattern above. Calculate the first and last terms of the ${20}^{\mathrm{th}}$ line.