Ashvikajain11idn
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(iii) [tex]$1+3+5+7+9+11+13+15+17+19+21+28$[/tex]

(i) Express 49 as the sum of 7 odd numbers.

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

Sagot :

GinnyAnsweridn
Sure, I'd be happy to help you break this down step by step:

### Part (iii)
The problem involves calculating the sum of a series of odd numbers:
[tex]\[ 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 28 \][/tex]
Let's sum these numbers in sequence:

[tex]\[ 1 + 3 = 4 \\ 4 + 5 = 9 \\ 9 + 7 = 16 \\ 16 + 9 = 25 \\ 25 + 11 = 36 \\ 36 + 13 = 49 \\ 49 + 15 = 64 \\ 64 + 17 = 81 \\ 81 + 19 = 100 \\ 100 + 21 = 121 \\ 121 + 28 = 149 \][/tex]

So, the total sum of these numbers is:
[tex]\[ 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 28 = 149 \][/tex]

### Part (i)
We want to express 49 as the sum of 7 odd numbers. The first 7 odd numbers are:
[tex]\[ 1, 3, 5, 7, 9, 11, 13 \][/tex]
Adding these together:
[tex]\[ 1 + 3 + 5 + 7 + 9 + 11 + 13 \][/tex]
Calculating step by step:
[tex]\[ 1 + 3 = 4 \\ 4 + 5 = 9 \\ 9 + 7 = 16 \\ 16 + 9 = 25 \\ 25 + 11 = 36 \\ 36 + 13 = 49 \][/tex]

Therefore, 49 can be expressed as the sum of the first 7 odd numbers:
[tex]\[ 49 = 1 + 3 + 5 + 7 + 9 + 11 + 13 \][/tex]

### Part (ii)
We want to express 121 as the sum of 11 odd numbers. The first 11 odd numbers are:
[tex]\[ 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21 \][/tex]
Adding these together:
[tex]\[ 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 \][/tex]
Calculating step by step:
[tex]\[ 1 + 3 = 4 \\ 4 + 5 = 9 \\ 9 + 7 = 16 \\ 16 + 9 = 25 \\ 25 + 11 = 36 \\ 36 + 13 = 49 \\ 49 + 15 = 64 \\ 64 + 17 = 81 \\ 81 + 19 = 100 \\ 100 + 21 = 121 \][/tex]

Therefore, 121 can be expressed as the sum of the first 11 odd numbers:
[tex]\[ 121 = 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 \][/tex]

I hope this detailed solution helps clarify the problem! If you have any other questions, feel free to ask.
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