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Question

The sum of first 20 terms of the sequence 0.7, 0.77, 0.777,...., is


A

781(1791020)

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B

79(991020)

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C

781(179+1020)

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D

79(99+1020)

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Solution

The correct option is C

781(179+1020)


Given sequence can be written as
710+77100+777103+...+ up to 20 terms
=7[110+11100+111103+...+upto20terms]
Multiply and divide by 9
79[(1110+(11102)+(11103))+.....up to 20 terms]=79[20110(1(110)20)1110]=79[1799+19(110)20]=781[179+(10)20]


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