## Method of Differences - Basic

Method of Differences is a way whereby the sum of a series is established under certain conditions

Q1. nth term of the series will be

•   (n2+n+1)/2
•  (n2+n+2)
•  (n2+n+2)/2
•   (n2+n+2)/2n

(n2+n+2)/2

Q2.  If tn denotes the nth term of the series then t50 is

•  492 - 1
•  492
•  502 + 2
•  493 + 2

493 + 2

Q3.  First term of the 11th group in the following groups (1), (2, 3, 4), (5, 6, 7, 8, 9), ..... is

•  89
•  97
•  101
•   123

101

Q4.  The sum of the series 6 + 66 + 666 + .... upto n terms is

•   2(10n+1 + 9n + 10)/27
•   2(10n+1 - 9n - 10)/27
•  2(10n+1 - 9n - 10)
•  None of these

2(10n+1 - 9n - 10)/27

Q5.  Sum of n terms of series 12 + 16 + 24 + 40 + .... will be

•  4(2n - 1)-n
•  2(2n - 1)-8n
•  (2n + 1)+8n
•  4(2n - 1)+8n

4(2n - 1)+8n

Q6.  If |a| is less than 1 and |b| is less than 1, then the sum of the series 1 + (1+a)b + (1+a+a2)b2 + (1+a+a2+a3)b3 + ...... is

•  1/(1-a)(1-ab)
•  1/(1-b)(1-a)
•  1/(1-b)(1-ab)
•  1/(1-a)(1-b)(1-ab)

1/(1-b)(1-ab)

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