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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.

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

Let the common difference of the given A. P. be d.
a = - 4
6th term = 6

$rightwards double arrow space space minus 4 plus left parenthesis 6 minus 1 right parenthesis straight d space equals 6 space space space space space space space space space space space space space left square bracket because space straight a subscript straight n equals straight a plus open vertical bar straight n minus 1 close vertical bar straight d right square bracket rightwards double arrow space space minus 4 plus 5 straight d equals 6 rightwards double arrow space space space space space space 5 straight d equals 6 plus 4 rightwards double arrow space space space space space space space 5 straight d space equals space 10 rightwards double arrow space space space space space space space space straight d equals 10 over 5 rightwards double arrow space space space space space space space space straight d space equals space 2$

Therefore,
Second term = -4 + 2 = -2
Third term = -2 + 2 = 0
Fourth term = 0 + 2 = 2
and, Fifth term = 2 + 2 = 4
Hence, the missing terms in the boxes are

$box enclose negative 2 end enclose comma space box enclose 0 comma space box enclose 2 comma space box enclose 4$

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38.

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

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