MathsGee Answers is Zero-Rated (You do not need data to access) on: Telkom | Dimension Data | Rain | MWEB
First time here? Checkout the FAQs!
x
MathsGee is Zero-Rated (You do not need data to access) on: Telkom |Dimension Data | Rain | MWEB

1 like 0 dislike
30 views
What is the sum of all two-digit odd positive numbers?
in Mathematics by Diamond (75,914 points) | 30 views

1 Answer

0 like 0 dislike
Best answer

Answer
2475


Explanation:
We know that smallest two digit odd number is 11, and the greatest two digit number is 99.

Since difference between consecutive odd numbers is 2 , these numbers form an arithmetic progression with first term $=11$, last term $=99$ and difference $=2$.

If there are total $\mathrm{N}$ terms in series, $\mathrm{N}^{\text {th }}$ term is given by $\mathrm{T}_{\mathrm{N}}=\mathrm{T}_{1}+(\mathrm{N}-1) \mathrm{d}$
$\Rightarrow 99=11+(\mathrm{N}-1)(2)$
$\Rightarrow 2(\mathrm{~N}-1)=99-11$
$2(\mathrm{~N}-1)=88$
$\Rightarrow \mathrm{N}-1=\frac{88}{2}$
$\Rightarrow \mathrm{N}=44+1$
$\Rightarrow \mathrm{N}=45$

Now sum of arithmetic progression can be found using standard formula,
$\mathrm{S}_{\mathrm{N}}=\left(\frac{\mathrm{N}}{2}\right)\left[2 \mathrm{~T}_{1}+(\mathrm{N}-1) \mathrm{d}\right.$
$\Rightarrow \mathrm{S}_{\mathrm{N}}=\left(\frac{45}{2}\right)[2 \times 11+(45-1)(2)]$
$\Rightarrow \mathrm{S}_{\mathrm{N}}=\left(\frac{45}{2}\right)[22+88]$
$\Rightarrow S_{N}=\left(\frac{45}{2}\right)[110]$
$\Rightarrow \mathrm{S}_{\mathrm{N}}=45 \times 55$
$\Rightarrow S_{N}=2475$

by Diamond (75,914 points)

Related questions

MathsGee provides answers to subject-specific educational questions for improved outcomes.



On MathsGee Answers, you can:


1. Ask questions
2. Answer questions
3. Comment on Answers
4. Vote on Questions and Answers
5. Donate to your favourite users

MathsGee Tools

Math Worksheet Generator

Math Algebra Solver

Trigonometry Simulations

Vectors Simulations

Matrix Arithmetic Simulations

Matrix Transformations Simulations

Quadratic Equations Simulations

Probability & Statistics Simulations

PHET Simulations

Visual Statistics

Other Tools

MathsGee ZOOM | eBook

16,915 questions
12,339 answers
122 comments
2,430 users