hey guys.....
find the missing terms with explainations :
1. 3,8,35,48,____,120
2. 3,6,24,30,63,72,____,132
3. 2,1,2,4,4,5,6,7,8,8,10,11,____
don't give unnecessary answers......
Answers
Answer:
1.) 2²-1 = 3
3³-1 = 8
6⁶-1 = 35
7⁷-1 = 48
10¹⁰-1 = 99
Answer is 99
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2.) the answer is 120 cause,
it's making a frequency like,
2²-1 = 3 again then adding to itself,
2²+2 = 6 again skipping 2
5²-1 means 24 again
5²+5 means 30 and the series continues and we end up as,
11²-1= 120 and then (←answer)
11²+11 = 132
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3.)
1st, 4th, 7th, 10th, 13th terms i.e. 2, 4, 6, 8, ?
II. 2nd, 5th, 8th, 11th terms i.e. 1, 4, 7, 10
III. 3rd, 6th, 9th, 12th terms i.e. 2, 5, 8, 11
Clearly, I consists of consecutive even numbers. So, the missing term is 10.
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Question (1) :- 3,8,35,48,____,120 .
Logic :-
→ 2² - 1 = 3
→ 3² - 1 = 8
→ 6² - 1 = 35
→ 7² - 1 = 48
→ x² - 1 = ?
→ 11² - 1 = 120
Now, See Logic For :- 2, 3, 6 , 7 , x , 11
Logic :- Alternate Add 4 .
→ 2 + 4 = 6
→ 3 + 4 = 7
→ 6 + 4 = 10 = x
→ 7 + 4 = 11.
So, we get x = 10 .
Hence, Answer = x² - 1 = 10² - 1 = 99 .
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Question (2) :-
3,6,24,30,63,72,____,132
Logic :-
→ 2² - 1 = 3
→ 2² + 2 = 6
→ 5² - 1 = 24
→ 5² + 5 = 30
→ 8² - 1 = 63
→ 8² + 8 = 72
→ x² - 1 = ?
→ 11² + 11 = 132
Logic For Next terms = +3.
So, X = 8 + 3 = 11 .
Hence, Answer = 11² - 1 = 121 - 1 = 120 .
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Answer (3) :-
2,1,2,4,4,5,6,7,8,8,10,11,____
Checking , Series with Next Two Terms we get :-
→ 2, 4 , 6 , 8 , 10, ?
→ 1, 4 , 7 , 10 ,
→ 2, 5, 8, 11 ,
So, Next Term with First Part = 10 + 2 = 12
→ Next Term with Second Part = 10 + 3 = 13.
→ Next Term with Third Part = 11 + 3 = 14.
Hence, Next Three Terms of series are (12, 13,14).