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For what value of n, are the with terms ...

For what value of n, are the with terms of two APs: 63, 65, 67, . . . and 3, 10, 17, . . . equal?

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For first A.P. : 63, 65, 67, ......
`a=63`
`d=65-63=67-65=2`
` :. " "a_(n)=63+(n-1)2=63+2n-2=2n+61`
For second A.P. :3, 10, 17, ......
`a=3`
`d=10-3=17-10=7`
`:. a_(n)=3+(n-1)7=3+7n-7=7n-4 `
Given that, `7n-4=2n+61`
`rArr 5n=65`
`rArr n=13`
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