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1.
The sum of n terms of an A.P. is 3n2 + n, find the nth term.
  • A.
    6n - 4
  • C.
    4n - 4
  • B.
    6n - 2
  • D.
    4n - 2
  • Answer & Explanation
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Answer : [B]
Explanation :
Given Sn = 3n2 + n, put n = 1, 2
S1 = 3.12 + 1 = 4
T1 = 4
S2 = 3.22 + 2 = 14
T2 = S2 - S1 = 14 - 4 = 10
 
  d = T2 - T1 = 10 - 4 = 6  
 
  Tn = a + (n -1) d = 4 + (n - 1) 6 = 6n - 2  
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2.
Find the sun of the following series
3 + 7 + 11 + 15 + . To 30 terms
  • A.
    1920
  • C.
    1970
  • B.
    1830
  • D.
    1740
  • Answer & Explanation
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Answer : [B]
Explanation :
The given series is 3 + 7 + 11 + 15 + to 30 terms.
a = 3, d = 4, n = 30
We know that
Sn =
n
2
 [2a + (n -1) d]  
S30 =
30
2
 [2 x 3 + (30 - 1) (4)]  
= 15 [6 + 116]
= 1830
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3.
Find the position of 62 in the following series 2, 5, 8, ....?
  • A.
    26
  • C.
    21
  • B.
    23
  • D.
    20
  • Answer & Explanation
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Answer : [C]
Explanation :
It is an A.P. series with a = 2, d = 3
Let 62 be the nth term.
 
 Tn = 62
But we know that Tn = a + (n 1) d
 
  62 = 2 + (n 1) 3      
or 62 = 2 + 3n 3
or 62 2 + 3 = 3n
or 63 = 3n
or 3n = 63
or n = 21
62 is the 21st term
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4.
If you save 1 paise totay, 2 paise next day and 3 paise the succeeding day and so on, what will be your savings in 365 days?
  • A.
    666.75
  • C.
    665.35
  • B.
    668.85
  • D.
    667.95
  • Answer & Explanation
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Answer : [D]
Explanation :
Savings on successive days are 1, 2, 3, 4 . Paise which form and A.P. with a = 1, d =1
 
  Total savings in 365 days
= S365 =
365
2
 [2 x 1 + (365 - 1) (1)]  
=
365
2
 [2 + 364]
=
365
2
 [366] = 365 x 183
= 66795 paise
= Rs. 667.95
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5.
Find the sun of the following series
72 + 70 + 68 + . + 40
  • A.
    886
  • C.
    952
  • B.
    918
  • D.
    988
  • Answer & Explanation
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Answer : [C]
Explanation :
The given series is 72 + 70 + 68 + .... + 40
a = 72, d = -2, l = 40
We know: l = a + (n 1) d, putting values of a, d and l
40 = 72 + (n 1) (-2) = 74 2n
or 2n = 34
 
  n = 17  
Now, we know that: Sn =
n
2
 [a + l]  
S17 =
17
2
 (72 + 40) =
17
2
 [112] = 17 x 56 = 952  
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