A. determine whether the sequence is arithmetic or not. If it is find the common difference and the next three terms. 1. 2,5,8,11,... 2. 2,-4,6,-8,10,... 3. - 6,-10,-14,-18,... 4. 40,42,44,46,... 5. 1.2,1.8,2.4,... 6. 1,5,9,13,...
Answers
1. The given sequence is:
2, 5, 8, 11 ,......
Determine whether the sequence is arithmetic or not. If it is find the common difference and the next three terms.
Here, first term (a) = 2
∴ Common difference (d) = 5 - 2 = 3
= 8 - 5 = 3
= 11 - 8 = 3
The common difference are same, the given sequence are in AP.
∴ Next three terms = 11 + 3, 11 + 2 × 3, 11 + 3 × 3
= 14, 17, 30
2. The given sequence is:
2, - 4, 6, - 8,10, .....
Determine whether the sequence is arithmetic or not. If it is find the common difference and the next three terms.
Here, first term (a) = 2
∴ Common difference (d) = - 4 - 2 = - 6
= 6 + 4 = 10
The common difference are same, the given sequence are in AP.
3. The given sequence is:
- 6, - 10, - 14, - 18, .....
Determine whether the sequence is arithmetic or not. If it is find the common difference and the next three terms.
Here, first term (a) = - 6
∴ Common difference (d) = - 10 - ( - 6) = - 10 + 6 = - 4
= - 14 - ( - 10) = - 14 + 10 = - 4
= - 18 - ( - 14) = - 18 + 4 = - 4
The common difference are same, the given sequence are in AP.
∴ Next three terms = - 18 - 4, - 18 + 2 × ( - 4), - 18 + 3 × (- 4)
= - 22, - 26, - 30
4. The given sequence is:
40, 42, 44, 46, ......
Determine whether the sequence is arithmetic or not. If it is find the common difference and the next three terms.
Here, first term (a) = 40
∴ Common difference (d) = 42 - 40 = 2
= 44 - 42 = 2
= 46 - 44 = 2
The common difference are same, the given sequence are in AP.
∴ Next three terms = 46 + 2, 46 + 2 × 2, 46 + 3 × 2
= 48, 50, 52
5. The given sequence is:
1.2, 1.8, 2.4, .......
Determine whether the sequence is arithmetic or not. If it is find the common difference and the next three terms.
Here, first term (a) = 1.2
∴ Common difference (d) = 1.8 - 1.2 = 0.6
= 2.4 - 1.8 = 0.6
The common difference are same, the given sequence are in AP.
∴ Next three terms = 2.4 + 0.6, 2.4 + 2 × 0.6, 2.4 + 3 × 0.6
= 3.0, 3.6, 4.2
6. The given sequence is:
1, 5, 9, 13 ...,...
Determine whether the sequence is arithmetic or not. If it is find the common difference and the next three terms.
Here, first term (a) = 1
∴ Common difference (d) = 5 - 1 = 4
= 9 - 5 = 4
= 13 - 9 = 4
The common difference are same, the given sequence are in AP.
∴ Next three terms = 13 + 4, 13 + 2 × 4, 13 + 3 × 4
= 17, 21, 25
Given : Different Sequence
2,5,8,11,...
2,-4,6,-8,10,...
- 6,-10,-14,-18,...
40,42,44,46,...
1.2,1.8,2.4,...
1,5,9,13,...
To Find : whether the sequence is arithmetic or not
if arithmetic then common difference and the next three terms
Solution:
AP is of form
a , a + d , a + 2d
2,5,8,11,...
5 = 2 + 3
8 = 2 + 2(3)
11 = 2 + 3(3)
This is an AP with d = 3
common difference = 3
Next three terms
14 , 17 , 20
2,-4,6,-8,10,...
difference
-6 , 10 , -14 , 18
This is not an AP
- 6,-10,-14,-18
common difference = - 4
next three terms
-22 , - 24 , - 26
40,42,44,46
common difference = 2
Next three terms
48 , 50 , 52
1.2,1.8,2.4
common difference = 0.6
Next three terms
3 , 3.6 , 4.2
1,5,9,13,...
common difference = 4
Next three terms
17 , 21 , 25
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