Addition of Odd Numbers

Q.

Without adding, find the sum. $\left(\mathrm{i}\right)1+3+5+7+9$

Q.

Question 8 (ii)
Express 121 as the sum of 11 odd numbers.

Q.

State true or false.

The sum of three odd numbers is even.

1. True
2. False

Q.

Question 129

A king wanted to reward his advisor, a wiseman of the kingdom. So, he asked the wiseman to name his own reward. The wise man thanked the king but said that he would ask only for some gold coins each day for a month. The coins were to be counted out in a pattern of one coin for the first day, 3 coins for the second day, 5 coins for the third day and so on for 30 days. Without making calculations, find how many coins will the advisor get in that month?

Q.

If $n$ is odd, then $1+3+5+7+.....+$ to $n$ terms is equal to

(a) $(n^2+1)$

(b) $(n^2-1)$

(c) $n^2$

(d) $(2n^2+1)$

Q.

Question 7 (i)
Without adding, find the sum:

1 +3 + 5+7 + 9

Q.

Question 7 (ii)
Without adding, find the sum:

1 +3 + 5+7 + 9 +11 +13+ 15 + 17+19

Q.

Using the numbers from 9 to 17, construct a 3 × 3 magic square. What is the magic sum here? What relation is there between the magic sum and the number in the central cell?

Q.

Using the given pattern, find the missing numbers.
$1^2+2^2+2^2=3^2$
$2^2+3^2+6^2=7^2$
$3^2+4^2+{12}^2={13}^2$
$4^2+5^2+..{.}^2={21}^2$
$5^2+..{.}^2+{30}^2={31}^2$
$6^2+7^2+...{.}^2=...{.}^2$.

Q.

(i)

Express $49$ as the sum of $7$ odd numbers.

(ii)

Express $121$ as the sum of $11$ odd numbers.

Q.

Question 7 (iii)
Without adding, find the sum:

1 +3 + 5+7 + 9 +11 +13+ 15 + 17+19 + 21 + 23

Q. Fill in the blanks in the following statement.
The number $(256{)}^{\frac{5}{7}}$ is .............^th root of ..........^th power of ...............

Q. Express $49$ as the sum of $7$ odd numbers.
Express $121$ as the sum of $11$ odd numbers.

1. $1+3+5+7+9+11$
   $1+3+5+7+9+11+13+15+19$
2. $1+3+5+7+9+11+13$
   $1+3+5+7+9+11+13+15+19+21$
3. $1+3+5+7+9+11$
   $1+3+5+7+9+11+13+15+19+21$
4. $1+3+5+7+9+11+13$
   $1+3+5+7+9+11+13+15+19$

Q. What happens when the power becomes 2 raised to -1

Q. Express 49 as the sum of 7 odd numbers.

Q.

Question 38

Fill in the blanks to make the statements true.

The sum of first six-odd natural numbers is ___

Q. Without adding find the sum
$1+3+5+7+9+11+13+15+17+19$

Q. Express 225 as the sum of odd numbers.

Q.

Question 7(iv)
Simplify:
(iv) $(-2{)}^3\times (-10{)}^3$

Q. Express $144$ as a sum of $12$ odd numbers.

Q. Without adding, find the sum
$1+3+5+7+9$
$1+3+5+7+9+11+13+15+17+19$
$1+3+5+7+9+11+13+15+17+19+21+23$

Q. Find the sum $1+3+5+.....+51$ (the sum of all odd numbers from $1$ to $51$) without actually adding them.

Q. Without addition find: $1+3+5+7+9+11+13+15+17+19+21+23+....+33$

Q.

The square of which of the following number will be odd numbers?
$\left(i\right)431$
$\left(ii\right)2826$
$\left(iii\right)7779$
$\left(iv\right)82004$

Q. Without adding, find the sum of 1 + 3 + 5 + 7 + 9 + 11.
[2 marks]

Q.

Using the numbers from 5 to 13, construct a 3 × 3 magic square. What is the magic sum here? What relation is there between the magic sum and the number in the central cell?

Q.

Without adding, find the sum of the following series:
1+3+5+7+9+11+13+15+17+19+21 =___

Q. A thief, after committing a theft runs at a uniform speed of $50$ m/minute. After $2$ minutes, a policeman runs to catch him. He goes $60m$ in first minute and increases his speed by $5$m/minute every succeeding minute. After how many minutes, the poilceman will catch the thief?

Q. Without adding, find the sum:
1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23

Q.

Without adding, find the sum of the following:

i.1+3+5+7+9+11+13+15+17+19+21 =___