Question

How many multiples of 5 lie between 10 and 2600 ?

Answer 1

Answer:

519

Step-by-step explanation:

it is related to arthematic progression..

where a- 10, d is 5 and tn is 2600

tn=a+(n-1)

formula...

2600=10+(n-1)5

=10+5n-5

=5n+5

2600-5=5n

2595=5n

therefore,n=519

please brainlist my answer

Answer 2

$\large\underline{\sf{Solution-}}$

We have to find multiples of 5 lies in between 10 and 2600

So, required multiples of 5 are 15, 20, 25, 30, _ _ _ _ _ , 2595,

which forms an Arithmetic Progression with

First term, a = 15

Common difference, d = 20 - 15 = 5

nᵗʰ term, aₙ = 2595

Wᴇ ᴋɴᴏᴡ ᴛʜᴀᴛ,

↝ nᵗʰ term of an arithmetic progression is,

$\begin{gathered}\red\bigstar\:\:{\underline{\orange{\boxed{\bf{\green{a_n\:=\:a\:+\:(n\:-\:1)\:d}}}}}} \\ \end{gathered}$

Wʜᴇʀᴇ,

aₙ is the nᵗʰ term.

a is the first term of the progression.

n is the no. of terms.

d is the common difference.

Tʜᴜs,

$\rm \: 15 + (n - 1)5 = 2595$

$\rm \: (n - 1)5 = 2595 - 15$

$\rm \: (n - 1)5 = 2580$

$\rm \: n - 1 = 516$

$\rm\implies \:n \: = \: 517$

So, there are 517 multiples of 5 lies in between 15 and 2595.

$\rule{190pt}{2pt}$

Additional Information :-

↝ Sum of n  terms of an arithmetic progression is,

$\begin{gathered}\red\bigstar\:\:{\underline{\orange{\boxed{\bf{\green{S_n\:=\dfrac{n}{2} \bigg(2 \:a\:+\:(n\:-\:1)\:d \bigg)}}}}}} \\ \end{gathered}$

Wʜᴇʀᴇ,

Sₙ is the sum of n terms of AP.

a is the first term of the progression.

n is the no. of terms.

d is the common difference.