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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?

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40.
Find the number of terms in each of the following APs :
7, 13, 19, . . . , 205

7, 13, 19, . . . , 205
Here, a = 7
d = 13 - 7 = 6
And, a_n= 205
Let the number of terms be n.
Then, a_n= 205
$rightwards double arrow$ a + ( n - 1) d = 205
$rightwards double arrow$ 7 + ( n - 1)6 = 205
$rightwards double arrow$ 6(n - 1) = 205 - 7
$rightwards double arrow$ 6(n - 1) = 198

$rightwards double arrow space space space space space n minus 1 equals 198 over 6$
$rightwards double arrow$ n - 1 = 33
$rightwards double arrow$ n = 33 + 1
$rightwards double arrow$ n = 34
Hence, the number of terms of the given A .P., is 34.