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Arithmetic Progressions

Short Answer Type

31.

Fill in the blanks in the following table, given that a is the first term, d the common difference and an the nth term of the AP:

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32.

Choose the correct choice in the following and justify :
30th term of the AP: 10, 7, 4, . . . , is
(A) 97 (B) 77 (C) –77 (D) – 87

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33.

Choose the correct choice in the following and justify :
30th term of the AP: 10, 7, 4, . . . , is

11th term of the A.P. is $space space minus 3 comma space 1 half comma space 2 comma space....$

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34.

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

$2. space square. space 26 space$

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35.

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

$square comma space 13. space square. space 3$

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36.

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

$5 comma space square comma space square comma space 9 1 half$

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37.

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

$negative 4 comma space square comma square comma space square comma square comma space 6$

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38.
In the following APs, find the missing terms in the boxes.

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

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
[∴ a_n = 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)
[∵ a_n = a + (n – 1) d] = 53 – 30 = 23
Fourth term = 53 + (4 – 1) (–15)
[∵ a_n = a + (n – 1) d] = 8
Fifth term = 53 + (5 – 1) (–15)
[∵ = a + (n – 1) d] = –7
Hence, the missing terms in the boxes are :

$box enclose 53 comma space box enclose 23 comma space box enclose 8 comma space box enclose negative 7 end enclose.$