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Arithmetic Progressions

Question
CBSEENMA10009833
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The 16th term of an AP is 1 more than twice its 8th term. If the 12th term of the AP is 47, then find its nth term.

Solution

Let a and d respectively be the first term and the common difference of the A.P.

we know that the nth term of an AP is given by  an = a + (n-1) d

According to the given information,

a16 = 1 + 2a8

⇒  a + (1 6- 1) d = 1 + 2[a + (8 - 1) d]

⇒   a + 15d = 1 + 2a + 14d

⇒  -a + d = 1                     ........(1) 

Also, it is given that, a12 = 47

⇒  a + ( 12 - 1 ) d = 47

⇒  a + 11d = 47                 .......(2)

Adding  (1) and (2), we have:

12d = 48

⇒  d = 4

From (1),

-a + 4 = 1  

⇒  a = 3

Hence,  an = a + (n - 1) d

                = 3 + (n - 1) (4)

                = 3 + 4n - 4

                = 4n - 1  

Hence, the nth term of the AP is  4n - 1.

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.

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

For the following APs, write the first term and the common difference
3, 1, – 1, – 3, . . .

For the following APs, write the first term and the common difference
– 5, – 1, 3, 7, . . .

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