Question

I would like to go to Temple and their are 100 stairs I will keep flowers on each stair as per the number of staiHow much flowers will I need? ​

Answer 1

GIVEN :-

• no of flowers = ( 1 + 2 + ....... + 100 )

TO FIND :-

• total no of flowers

SOLUTION :-

if we see the condition then we find an ap

( 1 ,2 , 3 ........ 100)

and number of flowers = sum of ap

now we know that sum of ap :-

$\implies \boxed{ \rm{sum \: of \: ap \: = \dfrac{n}{2}(a + l) }}$

where ,

n = total no of terms

a = first term

l = last term

so ,

n = 100

a = 1

l = 100

now put these values in formula

$\implies \rm{s _{n} \: = \dfrac{100}{2}(1 + 100)}$

$\implies \rm{s _{n} \: = \dfrac{100}{2}( 101)}$

$\implies \rm{s _{n} \: = {50}( 101)}$

$\implies \rm{ \bf{s _{n} \: = 5050}}$

hence ,

$\implies \boxed{\boxed{ \rm{total \: no \: of \: flowers = 5050} }}$

OTHER INFORMATION

we can use alternative formula for ap that is :-

• $\implies \rm{ \bf{s _{n} \: = \dfrac{n}{2}(2a+(n - 1) \: d)}}$

where ,

• sn = sum of all terms of ap

• n = total number of terms

• a = first term of ap

• d = difference of ap