# In the following Question, Rs. 33,000 is paid off in 12 instalments, such that each installment is Rs. 100 more than the preceding one. Find the amounts of the first and the last instalments.

Answer

Verified

381.9k+ views

Hint: The given question is in A.P., therefore we can consider the value of the number of terms to be 12, common difference to be 100 and then we can use these values to find the sum of n terms using the formula.

Complete step-by-step answer:

${S_n} = \dfrac{n}{2}\left[ {2a + \left( {n - 1} \right)d} \right]$.

Let, since we do not know the value of the first instalment, let the first instalment be a.

n = 12

d = 100

${S_{12}} = \dfrac{{12}}{2}\left( {2a + 11d} \right)$

$33000 = 6\left( {2a + 1100} \right)$

$2a + 1100 = 5500$

\[2a = 4400\]

\[a = 2200\]

So, the first instalment is Rs. 2200

Last instalment is 2200+11(100) = 2200+1100=3300

Note: In these questions where there is a common difference we can directly apply arithmetic progression formulas to find the answer.

Complete step-by-step answer:

${S_n} = \dfrac{n}{2}\left[ {2a + \left( {n - 1} \right)d} \right]$.

Let, since we do not know the value of the first instalment, let the first instalment be a.

n = 12

d = 100

${S_{12}} = \dfrac{{12}}{2}\left( {2a + 11d} \right)$

$33000 = 6\left( {2a + 1100} \right)$

$2a + 1100 = 5500$

\[2a = 4400\]

\[a = 2200\]

So, the first instalment is Rs. 2200

Last instalment is 2200+11(100) = 2200+1100=3300

Note: In these questions where there is a common difference we can directly apply arithmetic progression formulas to find the answer.

Recently Updated Pages

Define absolute refractive index of a medium

Find out what do the algal bloom and redtides sign class 10 biology CBSE

Prove that the function fleft x right xn is continuous class 12 maths CBSE

Find the values of other five trigonometric functions class 10 maths CBSE

Find the values of other five trigonometric ratios class 10 maths CBSE

Find the values of other five trigonometric functions class 10 maths CBSE

Trending doubts

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Difference Between Plant Cell and Animal Cell

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

What is pollution? How many types of pollution? Define it

Give 10 examples for herbs , shrubs , climbers , creepers

Which planet is known as the red planet aMercury bMars class 6 social science CBSE

Which state has the longest coastline in India A Tamil class 10 social science CBSE

Write a letter to the principal requesting him to grant class 10 english CBSE