Question

If 5+7+9+.......n=437 then n=

Answer 1

given :- a=5 , d=2 and tn=437

so,

tn=a+(n-1)d

437=5+(n-1)x2

437=5+2n-2

437-5=2n-2

432=2n-2

432+2=2n

434=2n

n=434/2

n=217

ans= n=217

Answer 2

The value of n is 19.

Step-by-step explanation:

Given : If 5+7+9+.......n=437

To find : The value of n ?

Solution :

The given sequence is arithmetic progression.

Here,

The first term is a=5

The common difference is d=7-5=2

The sum of the sequence is $S_n=437$

The sum of the sequence formula is

$S_n=\frac{n}{2}[2a+(n-1)d]$

$437=\frac{n}{2}[2(5)+(n-1)(2)]$

$437=n[5+n-1]$

$437=n[4+n]$

$437=4n+n^2$

$n^2+4n-437=0$

$n^2+23n-19n-437=0$

$n(n+23)-19(n+23)=0$

$(n-19)(n+23)=0$

$n=19,-23$

Reject the negative value.

The value of n is 19.

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