Arithmetic Progressions

Question

For what value of n, are the nth terms of two APs: 63, 65, 67, . . . and 3, 10, 17, . . . equal?

Solution

Given A .P.s are :
63, 65, 67, ... and 3, 10, 17, ...
Here, a₁ = 63, a₂ = 65, a₃ = 67, ....
and 6, = 3, b₂ = 10, b₃ = 17.....
Let d₁ and d₂ be the common differences of two given A .P.s respectively. Then
d₁ = 65 – 63 = 67 – 65 = 2
and d₂ = 10 – 3 = 17 – 10 = 7
Now, nth term of the 1st A .P. = a₁ + (n – 1)d₁and nth term of the Ilnd A.P. = b₁ + (n – 1 )d₂∵ nth terms of the given two A .P.s are equal.
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$rightwards double arrow$ 63 + (n - 1) x 2 = 3 + (n - 1) x 7
$rightwards double arrow$ 63 + 2n -2 = 3 + 7n - 7
$rightwards double arrow$ 2n + 61 = 7n - 4
$rightwards double arrow$ 7n - 2n = 61 + 4
$rightwards double arrow$ 5n = 65
$rightwards double arrow$ $straight n space equals space 65 over 5 equals 13$
Hence, the required value of n = 13.

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

For what value of n, are the nth terms of two APs: 63, 65, 67, . . . and 3, 10, 17, . . . equal?

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

For what value of n, are the nth terms of two APs: 63, 65, 67, . . . and 3, 10, 17, . . . equal?

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

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