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Question

The nth term of a sequence of numbers is an and given by the formula an=an1+2n for n2 and a1=1.
The sum of first 20 terms is

A
3060
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B
3059
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C
2680
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D
2679
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Solution

The correct option is A 3060
a1=1a2=a1+4=5a3=a2+6=11a4=a3+8=19

Now,
S=1+5+11+19++an
S= 1+5+11++an1+an
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯0=1+4+6+8++(anan1)an
an=1+4+6+8++(anan1)(n1) terms

an=1+2(n1)2[4+(n2)]an=1+(n1)(n+2)an=n2+n1an=n(n+1)1Sn=nr=1[r(r+1)1]Sn=nr=1r(r+1)nr=11Sn=n(n+1)(n+2)3nS20=20(21)(22)320S20=3060

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