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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 $space space minus 3 comma space 1 half comma space 2 comma space....$

The given A. P. is $space space minus 3 comma space 1 half comma space 2 comma space....$
Here, a = -3
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and n = 11
We know that a_n= a + (n - 1) d
$S o comma space space space space space space space space space a subscript 11 equals negative 3 plus open parentheses 11 minus 1 close parentheses open parentheses 5 over 2 close parentheses rightwards double arrow space space space space space space space space space space a subscript 11 equals negative 3 plus 25 rightwards double arrow space space space space space space space space space space a subscript 11 space equals space 22$
Hence, the correct choice is (B) 22.

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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.

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