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Meaning of the Series
The notion of sequences may be used to define series in mathematics. Because sequence and series are two notions that are intertwined. Assume a1, a2, a3,..., an is a sequence, then the phrase a1 + a2 + a3 +,...+ an is referred to as the series associated with the sequence. Depending on whether the above sequence is finite or infinite, the series is finite or infinite. To illustrate the summation involved, series are frequently expressed in compact form, known as sigma notation, which uses the Greek symbol sigma.
Series Number
A series can have several terms in the form of numerical values, functions, quantities, and so on. The symbolized amount, not the total itself, is indicated when the series is supplied. 2 + 4 + 6 + 8 + 10 + 12 is a six-term sequence, for example. To get the total of these numbers, we use the term "sum of a series," which refers to the number that is obtained by adding the series' terms together; the sum of the series is 42.
Finite Series
A finite series is a series having a limited number of terms.
If a1 + a2 + a3 +... + an is an n-term series, then it is a finite series with n terms.
As a result, Sn stands for the sum of the series and is written as:
Sn = ∑ an
We may also specify the total of a certain number of terms. These are written as follows:
S1 = a1
S2 = a1 + a2
S3 = a1 + a2 + a3
S4 = a1 + a2 + a3 + a4
….
Sn = a1 + a2 + a3 + … + an
Questions And Answers
Question 1
Find the missing number from the given responses
1, 0.125, 1/27, 1/64, ?, 1/216
Option1: 0.025
Option 2: 1/8
Option 3: 1/128
Option 4: 0.008
Answer:
4: 0.008
Explanation:
cube of 1 ,2 ,3 ,4 ,5 ,6 in denominator.
Question 2
Find the missing number from the given responses
–1,0,?,8,15.,24
Option 1: 4
Option 2: 3
Option3: 2
Option4: 1
Answer:
2: 3
Explanation:
square of 0,1,2,3,4,5andsubstract1.
Question 3
Find the missing number from the given responses
0,6,24,60,?,210
Option 1: 117
Option 2: 119
Option 3: 120
Option 4: 153
Answer:
3: 120
Question 4
Find the missing number from the given responses
–1,2,7,?,23,34,47
Option1: 13
Option 2: 14
Option 3: 12
Option4: 15
Answer:
2: 14
Explanation:
-1 → +32 → +57 → +714 → +923 → +1134 → +1347hence 14 is the right ans.
Question 5
Find the missing number from the given responses
0.01, 0.04, 0.09, ?
Option 1: 0.016
Option 2: 1.6
Option 3: 0.16
Option4: 0.106
Answer:
3: 0.16
Explanation:
square of .1, .2, .3, .4
Question 6
Find the missing number from the given responses
6,24,12,?,18,8,24,0
Option1: 14
Option 2: 18
Option 3: 16
Option 4: 20
Answer:
3: 16
Question 7
Find the missing number from the given responses
0.15, 0.3, ?, 1.2, 2.4
Option 1: 0.6
Option 2: 0.9
Option3: 0.06
Option 4: 4.8
Answer:
1: 0.6
Explanation:
multiply each term with 2 .
Question 8
Find the missing number from the given responses 3,8,18,35,?,98
Option 1: 61
Option 2: 71
Option 3: 41
Option 4: 51
Answer:
1: 61
Explanation:
The sequence can be explained by looking at the difference between the numbers. Between 3 and 8 is 5..... which is a 4+1, a perfect square plus 1
Between 8 and 18 is 10... which 9+1, the next perfect square plus 1
Between 18 and 35 is 17... which 16+1, the next perfect square plus 1
So.... the between 35 and X ... will be 25 +1, which is 26 35+26=61
So, the answer is 61.
Oh, by the way, the sequence continues, so 61 + 36+1 = 98. 61 is the answer.
Question 9
Find the missing number from the given responses
39, 169, 299, ?
Option 1: 339
Option 2: 429
Option 3: 519
Option 4: 609
Answer:
2: 429
Explanation:
add +130 in each term .
Question 10
Find the missing number from the given responses.
2460, 3570, 4680, ?
Option1: 8640
Option 2: 5670
Option 3: 5970
Option 4: 5790
Answer:
4: 5790
Explanation:
Question 11
Find the missing number from the given responses.
321, 301, ?, 181, 21
Option 1: 281
Option 2: 161
Option 3: 241
Option4: 261
Answer:
4: 261
Explanation:
321-20=301
301-40=261
261-80=181 181-160=21
Question 12
Find the missing number from the given responses.
49, 64, ?, 100, 121
Option 1: 74
Option 2: 80
Option 3: 75
Option 4: 81
Answer:
4: 81
Explanation:
square of 7,8,9,10,11,.
Question 13
Find the missing number from the given responses.
4, 5.2, 6.4, ?, 8.8
Option1: 7
Option 2: 8
Option 3: 7.6
Option 4: 8.25
Answer:
3: 7.6
Explanation:
add +1.2 in each term
Question 14
Find the missing number from the given responses.
2, 8, 40, ?, 1680, 13440
Option1: 80
Option 2: 120
Option 3: 160
Option4: 240
Answer
4: 240
Explanation:
multiply by 4,5,6,7,8, respectively
Question 15
Find the missing number from the given responses.
21, 26, 33, 42, 53, ?
Option 1: 56
Option 2: 63
Option 3: 66
Option 4: 69
Answer
3: 66
Explanation:
add +5 , +7, +9, +11, +13 respectively.
Question 16
Find the missing number from the given responses.
6,?,15,27,51,99
Option 1: 10
Option 2: 9
Option 3 :11
Option4: 12
Answer:
2: 9
Explanation:
6 × 2 = 12 - 3 = 99 × 2 = 18 - 3 = 1515 × 2 = 30 - 3 = 2727 × 2 = 54 - 3 = 5151 × 2 = 101 - 3 = 99
Question 17
Find the missing number from the given responses. 5, 13, 29, 61, 125, ?
Option 1: 253
Option 2: 196
Option 3: 245
Option 4: 145
Answer: 1: 253
Explanation:
multiply by 2 and add 3 in each term .
Question 18
Find the missing number from the given responses 242, 393, 4164, ?
Option1: 5525
Option 2: 5255
Option 3: 5235
Option 4: 5325
Answer:
2: 5255
Explanation:
242, 393, 4164, ?
Ist series 2, 3, 4, 5 IIndseries4,4+5=9,9+7=16,16+9=25 ∴ the answer is 5255.
Question 19
Find the missing number from the given responses.
3,5,8,13,21,34,55,?,
Option 1: 34
Option 2: 55
Option 3: 21
Option 4: 89
Answer:
4: 89
Explanation:
3+5=8 5+8=13 8+13=21 13+21=34 21+34=55 34+55=89
Question 20
Find the missing number from the given responses.
313, 623, 933, 1243, ?
Option 1: 1863
Option 2: 2173
Option 3: 1553
Option 4: 2483
Answer:
3: 1553
Explanation:
add 310 in each term