An algebra problem by Srinidhi U.S

Algebra Level 2

1+3+5+7+9+.................+nth

find the nth term?

n+1 n(n+1) n(2n -1) 2n - 1 n

2 solutions

The Adammz
Aug 30, 2015

It shows an arithmetic progress. So we can use this formula:

${ T }_{ n }=a+(n-1)d$

"a" is equal to the first term. So...

$a=1$

"d" is the difference between two consecutive terms... or something.

$d=3-1=2$ or $d=5-3=2$ or $d=7-5=2$

Substitute them into the formula...

${ T }_{ n }=1+(n-1)2$

${ T }_{ n }=1+2n-2$

${ T }_{ n }=2n-1$

Adam Phúc Nguyễn
Aug 30, 2015

$\displaystyle 2n-1$ is odd for $n \in \mathbb{N}, n>0$ . $2n$ divisible by 2 so we must minus 1.

Why not $\displaystyle +1$ ? It's be true, but for $\displaystyle \geq 0$ .

I guess it's because it shows an arithmetic progression. We know that the second term in this a.p. is 3. Because 2n-1 = 2(2)-1 = 3. So if we use 2n+1 instead, we would get the third term and not the second term.

I request the guy who made this question to put 2n+1! Just to confused some people! :D

The AdamMZ - 5 years, 9 months ago

An algebra problem by Srinidhi U.S

2 solutions

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