(1) In each of the arithmetic sequences below, some terms are missing and
their positions are marked with O. Find them.
1) 24, 42, O, O,...
i) O, 24, 42, O,...
iii) O.O, 24, 42, ...
iv) 24, O, 42, O,...
v) 0,24, 0, 42, ...
vi) 24, O, O, 42, ...
Answers
Answer:
24
42
0
24
0
0
this is complete sequence
Answer:
1) 24,42,60,78,..
i) 6,24,42,60,...
iii) -12, 6,24,42,....
iv) 24,33,42,51,....
v) 15, 24,33,42,.....
vi) 24,30,36,42,.....
Step-by-step explanation:
Given that the sets are in arithmetic sequences.
Recall the concept,
In an arithmetic sequence, the difference between two consecutive terms is constant.
1) 24,42, O,O,........
here we have,
first term = 24
Second term = 42
common difference = 42 -24 = 18
Hence the third term = 42+18 = 60
Fourth term =60+18 = 78
The missing terms are 60 and 78
The sequence is 24,42,60,78,..
i) O, 24, 42, O,...
Second term = 24
Third term = 42
Common difference = 42 -24 = 18
First term = 24 -18 = 6
Fourth term = 42 +18 = 60
Hence the missing terms are 6 and 60
The sequence is 6,24,42,60,...
ii) O,O, 24, 42, ...
Third term = 24
Fourth term = 42
Common difference = 42 -24 = 18
second term = 24 -18 = 6
First term = 6 - 18 = -12
Hence the missing terms are -12 and 6
The sequence is -12, 6,24,42,....
iv) 24, O, 42, O,...
First term = 24
Third term = 42
2×Common difference = 42 -24 = 18
common difference = 9
second term = 24 +9 = 33
Fourth term = 42+9 = 51
Hence the missing terms are 33 and 51
The sequence is 24,33,42,51,....
v) 0,24, 0, 42, ...
Second term = 24
Fourth term = 42
2×Common difference = 42 -24 = 18
common difference = 9
First term = 24 -9 = 15
Third term = 24+9 = 33
The missing terms are 15 and 33
The sequence is 15, 24,33,42,.....
vi) 24, O, O, 42, ...
First term = 24
Fourth term = 42
3 ×common difference = 42-24 =18
common difference = 6
Second term = 24+6 = 30
Third term = 30+6 =36
The missing terms are 30,36
The sequence is 24,30,36,42,.....
Hence, the answer is
1) 24,42,60,78,..
i) 6,24,42,60,...
iii) -12, 6,24,42,....
iv) 24,33,42,51,....
v) 15, 24,33,42,.....
vi) 24,30,36,42,.....
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