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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.

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

Let the first term and the common difference of the given A .P. be a and b respectively.
Second term = 13
⇒ a + (2 – 1) d = 13
⇒ a + d = 13 ...(i)
Fourth term = 3
⇒ a+ (4 – 1)d = 3
⇒ a + 3d = 3 ...(ii)
Solving (i) and (ii), we get
a = 18
d = –5
Therefore,
Third term = a + (3 – 1)d
= a + 2d
= 18 + 2(–5)
= 18 –10 = 8
Hence, the missing terms in the boxes are $space space space space box enclose 18 space and space box enclose 8.$

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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.

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