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Arithmetic Progressions

Question
CBSEENMA10007523
Wired Faculty App

In the following APs, find the missing terms in the boxes.

square comma space 38 comma space square comma space square comma space square comma space minus 22.





Solution

Let the first terms and the common difference of the given A .P. be a and d respectively.
Second term = 38
⇒ a + (2 – 1)d = 38
[∴ an = a + (n – 1) d]
⇒ a + d = 38 ...(i)
⇒ Sixth term = –22
⇒ a + (6 – 1 )d = –22
⇒ a + 5d = –22 ...(ii)
Solving (i) and (ii), we get
a = 53 d = –15
Therefore,
Third term = 53 + (3 –1 (–5)
[∵ an = a + (n – 1) d] = 53 – 30 = 23
Fourth term = 53 + (4 – 1) (–15)
[∵ an = a + (n – 1) d] = 8
Fifth term = 53 + (5 – 1) (–15)
[∵ = a + (n – 1) d] = –7
Hence, the missing terms in the boxes are :
box enclose 53 comma space box enclose 23 comma space box enclose 8 comma space box enclose negative 7 end enclose.

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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