Question

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Answer 1

Given Question

A person borrows ₹ 3000 and agrees to pay with a total interest of ₹ 480 in 12 monthly instâllment. Each instâllment being more than the preceeding one by ₹ 40. Find the amount of first instâllment and last instâllment.

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

Given that

A person borrows ₹ 3000 and agrees to pay with a total interest of ₹ 480 in 12 monthly instâllment. Each instâllment being more than the preceeding one by ₹ 40.

So, Let assume that

First instâllment be ₹ x

Second instâllment be ₹ x + 40

Third instâllment be ₹ x + 80

This implies, sequence of instâllment form an Arithmetic sequence with First term x and common difference 40.

Now, Amount to be paid in 12 instâllment = ₹ 3480

Wᴇ ᴋɴᴏᴡ ᴛʜᴀᴛ,

↝ Sum of n  terms of an arithmetic sequence 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 sequence.

n is the no. of terms.

d is the common difference.

So, here we have

$\purple{\rm :\longmapsto\:a = x}$

$\purple{\rm :\longmapsto\:d= 40}$

$\purple{\rm :\longmapsto\:n= 12}$

$\purple{\rm :\longmapsto\:S_n= 3480}$

So, on substituting the values, we get

$\rm :\longmapsto\:3480 = \dfrac{12}{2} \bigg(2x + (12 - 1)40 \bigg)$

$\rm :\longmapsto\:3480 = 6 \bigg(2x + 440 \bigg)$

$\rm :\longmapsto\:580 = 2x + 440$

$\rm :\longmapsto\:580 - 440= 2x$

$\rm :\longmapsto\:2x = 140$

$\bf\implies \:x = 70$

So, Amount of first instâllment = ₹ 70

Wᴇ ᴋɴᴏᴡ ᴛʜᴀᴛ,

↝ nᵗʰ term of an arithmetic sequence 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 sequence.

n is the no. of terms.

d is the common difference.

Tʜᴜs,

$\purple{\rm :\longmapsto\:a_{12}}$

$\rm \:  =  \: a + (12 - 1)d$

$\rm \:  =  \: a + 11d$

$\rm \:  =  \: 70+ 11 \times 40$

$\rm \:  =  \: 70+ 440$

$\rm \:  =  \: 510$

Hence,

$\begin{gathered}\begin{gathered}\bf\: \bf\implies \:Amount \: of \: \begin{cases} &\sf{ {1}^{st} \: instâllment = 70 } \\ \\ &\sf{ {12}^{th} \: instâllment = 510} \end{cases}\end{gathered}\end{gathered}$

Answer 2

Answer:

• 1st ínstäľľment = ₹70
• Last ínstäľľment = ₹510

Step-by-step explanation:

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