Question

solve this equation 1+3+5..............+x = 10000​

Answer 1

we can find that the equation add only odd terms

now we should how many terms are there .the sum of n terms in odd series are n*2=10000

n=100

by formula the sum of term in ap if the odd series are in ap then the formula is. summ =n/2( first term +last term)

so there are 100 terms

10000=100/2(1+x

10000(2)/100=1+x

200=1+x

x=199

now formula

Answer 2

Solution :-

◾Given Question :-

⏩1 + 3 + 5 .... + x = 10000

◾Let us consider this series .

◾The difference between two consecutive numbers in series.

▪️Between 1 and 3

= 3-1

= 2

▪️Between 3 and 5

= 5 - 3

= 2

◾So we can say that it is a A.P , With

▪️a = 1

▪️d = 2 (common difference)

◾Now as we know that the sum of A.P

$S_n = \dfrac{n}{2} (2a + (n-1)d)$

So as sum = 10000

$\implies 10000 = \dfrac{n}{2} (2(1) + (n-1)2)$

$\implies 10000 = \dfrac{n}{2} (2 + 2n - 2 )$

$\implies 10000 = \dfrac{n}{2} \times 2n$

$\implies n^2 = 10000$

$\implies n = \sqrt{10000} \\\\ \implies n = 100$

▪️So the no of term = 100

◾So as we know

nth term of AP = a + (n-1)d

→ x = 1 + (100 -1)× 2

→ x = 1 + (99) × 2

→ x = 1 + 198

→ x = 199

So , x = 199