Question

A person buys National Savings Certificates every
year of value exceeding the last year’s purchase by
Rs. 200. After 10 years he finds that the total
value of the certificates is Rs. 10,500. Find the
value of the certificates purchased by him in the
first year and in the seventh year.

Answer 1

Answer: hope you will understand

Step-by-step explanation:

Answer 2

The value of the certificates purchased by person in the 1st year and   the 7th  year is Rs. 150 and Rs. 1350 respectively.

Step-by-step explanation:

Given:

National Savings Certificates bought by a person every year of value exceeding the last year’s purchase by Rs. 200.

After 10 years the total value of the  purchased certificates is Rs. 10,500

To Find:

The value of the certificates purchased by person in the 1st year.

The value of the certificates purchased by person in the 7th  year.

Formula Used:

$Zn=\frac{n}{2}[2p+(n-1) q]$               ------------------------------ formula no.01

$Yn=p+(n-1)q$                ------------------------------------- formula no.02

Where,

Yn = the value of the certificates purchased  in nth  year of  an Arithmetic Progression.

Zn= the total value of the certificates after n years of an Arithmetic Progression.

p=  the value of the certificates purchased in the first year

q=  the difference between the value of the certificates.

n = the number of terms.

Solution:

As given- National Savings Certificates bought by a person every year of value exceeding the last year’s purchase by Rs. 200.

  q=200

As given- after 10 years the total value of the  purchased certificates is Rs. 10,500

  n =10 years  and Zn =10500

Since, it follows Arithmetic progression.

Applying the formula no.01.

$Zn=\frac{n}{2}[2p+(n-1) q]$

Putting the values of q, n  and  Zn we get.

$10500=\frac{10}{2}[2p+(10-1) \times200]$

$10500= 5[2p+1800]$

$2100=2p+1800$

$300=2p$

$p=Rs. 150$

The value of the certificates purchased in the 1st  is Rs.150.

To find - The value of the certificates purchased by person in the 7th  year is

Applying formula no.01.

$Yn=p+(n-1)q$

Putting values of p=150,q= 200 and n =7 , we get.

$Yn=150+(7-1)\times 200$

   $= 150+ 1200$

   $= Rs. 1350$

The value of the certificates purchased by person in the 7th  year is  Rs.1350.

Thus, The value of the certificates purchased by person in the 1st year and   the 7th  year is Rs. 150 and Rs. 1350 respectively.