Tanvika purchases every year National Saving Certificates of value exceeding the last year purchases by Rs. 25. After 20 years, he find the total value of certificates purchased by him is Rs. 7250. Find the value of the certificates purchased.

(i) in the first year. (ii) in the 12th year.

Solution

Let the value of certificates purchased in the first year be Rs. ‘a’ and annual increase = Rs.25. Here, first term = a, d = 25, S₂₀ = 7250.
We know that,

straight S subscript straight n equals straight n over 2 left square bracket 2 straight a space plus left parenthesis straight n minus 1 right parenthesis straight d right square bracket rightwards double arrow space straight S subscript 10 equals 20 over 2 left square bracket 2 straight a plus left parenthesis 20 minus 1 right parenthesis 25 right square bracket rightwards double arrow space 7250 space equals space 10 space left parenthesis 2 straight a plus 19 cross times 25 right parenthesis

⇒ 7250 = 10 (2a + 475)
⇒ 725 = 2a + 475 ⇒ 2a = 250
⇒ a = 125
Hence, the value of certificates purchased in first year = Rs. 125.
Now, value of certificates purchased in 12th year.
a₁₂ = a + (12 – 1 )d = 125 + (11) (25) = 125 + 275 = Rs. 400.

Some More Questions From Arithmetic Progressions Chapter

In which of the following situational, does the list of numbers involved make an arithmetic progression, and why?

The cost of digging a well for the first metre is Rs. 150 and rises by Rs. 50 for each succeeding metre.

In which of the following situational, does the list of numbers involved make an arithmetic progression, and why?

The taxi fare after each km when the fare is Rs. 15 for the first km and Rs. 8 for each additional km.

In which of the following situational, does the list of numbers involved make an arithmetic progression, and why?

The cost of digging a well for the first metre is Rs. 150 and rises by Rs. 50 for each succeeding metre.

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Arithmetic Progressions

Tanvika purchases every year National Saving Certificates of value exceeding the last year purchases by Rs. 25. After 20 years, he find the total value of certificates purchased by him is Rs. 7250. Find the value of the certificates purchased.

(i) in the first year. (ii) in the 12th year.

Some More Questions From Arithmetic Progressions Chapter

In which of the following situational, does the list of numbers involved make an arithmetic progression, and why?

The cost of digging a well for the first metre is Rs. 150 and rises by Rs. 50 for each succeeding metre.

In which of the following situational, does the list of numbers involved make an arithmetic progression, and why?

The taxi fare after each km when the fare is Rs. 15 for the first km and Rs. 8 for each additional km.

In which of the following situational, does the list of numbers involved make an arithmetic progression, and why?

The cost of digging a well for the first metre is Rs. 150 and rises by Rs. 50 for each succeeding metre.

Write first four terms of the AP, when the first term a and the common difference d are given as follows:
a – 10, d = 10

Write first four terms of the AP, when the first term a and the common difference d are given as follows:
a = –2, d = 0

Write first four terms of the AP, when the first term a and the common difference d are given as follows:
a = 4, d = – 3

Write first four terms of the AP, when the first term a and the common difference d are given as follows:

a = – 1.25, d = – 0.25

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For Daily Free Study Material Join wiredfaculty

Arithmetic Progressions

Tanvika purchases every year National Saving Certificates of value exceeding the last year purchases by Rs. 25. After 20 years, he find the total value of certificates purchased by him is Rs. 7250. Find the value of the certificates purchased. (i) in the first year. (ii) in the 12th year.

Some More Questions From Arithmetic Progressions Chapter

In which of the following situational, does the list of numbers involved make an arithmetic progression, and why?The cost of digging a well for the first metre is Rs. 150 and rises by Rs. 50 for each succeeding metre.

In which of the following situational, does the list of numbers involved make an arithmetic progression, and why?The taxi fare after each km when the fare is Rs. 15 for the first km and Rs. 8 for each additional km.

In which of the following situational, does the list of numbers involved make an arithmetic progression, and why?The cost of digging a well for the first metre is Rs. 150 and rises by Rs. 50 for each succeeding metre.

Write first four terms of the AP, when the first term a and the common difference d are given as follows:a – 10, d = 10

Write first four terms of the AP, when the first term a and the common difference d are given as follows:a = –2, d = 0

Write first four terms of the AP, when the first term a and the common difference d are given as follows:a = 4, d = – 3

Write first four terms of the AP, when the first term a and the common difference d are given as follows:a = – 1.25, d = – 0.25

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Tanvika purchases every year National Saving Certificates of value exceeding the last year purchases by Rs. 25. After 20 years, he find the total value of certificates purchased by him is Rs. 7250. Find the value of the certificates purchased.

(i) in the first year. (ii) in the 12th year.

In which of the following situational, does the list of numbers involved make an arithmetic progression, and why?

The cost of digging a well for the first metre is Rs. 150 and rises by Rs. 50 for each succeeding metre.

In which of the following situational, does the list of numbers involved make an arithmetic progression, and why?

The taxi fare after each km when the fare is Rs. 15 for the first km and Rs. 8 for each additional km.

In which of the following situational, does the list of numbers involved make an arithmetic progression, and why?

The cost of digging a well for the first metre is Rs. 150 and rises by Rs. 50 for each succeeding metre.

Write first four terms of the AP, when the first term a and the common difference d are given as follows:
a – 10, d = 10

Write first four terms of the AP, when the first term a and the common difference d are given as follows:
a = –2, d = 0

Write first four terms of the AP, when the first term a and the common difference d are given as follows:
a = 4, d = – 3

Write first four terms of the AP, when the first term a and the common difference d are given as follows:

a = – 1.25, d = – 0.25