Show that a₁ , a₂ , . . ., a_n, . . . form an AP where an is defined as below :
a_n = 9 – 5n

Solution

It is given that :
a_n = 9 – 5n
a₁ = 9 – 5(1) = 9 – 5 = 4
a₂ = 9 – 5 (2) = 9 – 10 = –1
and a₃ = 9 – 5(3) = 9 – 15 = –6
Now, we have following numbers :
4, –1,–6, –11,.........
Since, the difference between each pair of consecutive terms are constant.
So, the given numbers form an A.P.
Here, a = 4, d = –5, n = 15
$We space know comma space space space space space space straight S subscript straight n space equals straight n over 2 left square bracket 2 straight a space plus left parenthesis space straight n minus 1 right parenthesis straight d right square bracket space space space space space space space space space space space space space space space space space space So comma space space straight S subscript 15 equals 15 over 2 left square bracket 2 cross times 4 plus 915 minus 109 minus 50 right square bracket space space space space space space space space space space space space space space space space space equals 15 over 2 left square bracket 8 minus 70 right square bracket equals 15 over 2 cross times negative 62 space space space space space space space space space space space space space space space space space equals 15 cross times negative 32 equals negative 480$

Some More Questions From Arithmetic Progressions Chapter

In which of the following situations, 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.

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.

For Daily Free Study Material Join wiredfaculty

Arithmetic Progressions

Show that a₁ , a₂ , . . ., a_n, . . . form an AP where an is defined as below :
a_n = 9 – 5n

Some More Questions From Arithmetic Progressions Chapter

In which of the following situations, 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.

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

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Phone Number

Email Address

Loaction

For Daily Free Study Material Join wiredfaculty

Arithmetic Progressions

Show that a1 , a2 , . . ., an, . . . form an AP where an is defined as below :an = 9 – 5n

Some More Questions From Arithmetic Progressions Chapter

In which of the following situations, 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.

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

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Show that a₁ , a₂ , . . ., a_n, . . . form an AP where an is defined as below :
a_n = 9 – 5n

In which of the following situations, 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.

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