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Consider the pattern shown below: {:("...

Consider the pattern shown below:
`{:(" Row ",1,1,,,),(" Row ",2,3,5,,),(" Row ",3,7,9,11,),(" Row ",4,13,15,17,19):}etc.`
The number at the end of row 60 is

A

3659

B

3519

C

3681

D

3731

Text Solution

Verified by Experts

The correct Answer is:
A
If last term of nth row is `T_(n)`, then
Let `S=1+5+11+19+"...."T_(n)`
`(S=ul1+ul5+ul11+ul19+"....+"ulT_(n-1)+ulT_(n))/(0=1+4+6+8"....."n" terms "-T_(n))`
`T_(n)=1+2(2+3+4+"....."(n-1)" terms" )` ,brgt `=1+2((n-1))/(2)[2*2+(n-2)*1]`
`=1+(n+1)(n+2)`
`=1+n^(2)+n-2`
`implies T_(n)= n^(2)+n-1`
`:. T_(60)=(60)^(2)+60-1=3600+59=3659`.
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