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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.

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

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39.
Which term of the AP : 3, 8, 13, 18, . . . ,is 78?

The given A. P. is 3, 8, 13, 18, .....
Here, a = 3
d = 8 - 3 = 5
Let the nth term f=of the A. P. be 78
Then, a_n= a + (n - 1)d
$space space rightwards double arrow space space space$ 78 = 3 + (n -1) (5)
$rightwards double arrow$ 5(n - 1) = 78 - 3
$rightwards double arrow$ 5 (n - 1) = 75

$rightwards double arrow space space space space space space n minus 1 equals 75 over 5$
$rightwards double arrow$ n - 1 = 15
$rightwards double arrow$ n = 15 + 1
$rightwards double arrow$ n = 16
Hence, 16th term of the A .P. is 78.