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Question
Find the common difference and 99th term of the arithmetic progression:
`7 3/4, 9 1/2, 11 1/4, ................`
Solution
The given A.P. is `7 3/4, 9 1/2 , 11 1/4, ................`
i.e `31/4, 19/2, 45/4, .........`
Common difference = d
= `19/2 - 31/4`
= `(38 - 31)/4`
= `7/4`
= `1 3/4`
First term = a = `31/4`
The general term of an A.P. is given by
tn = a + (n – 1)d
`=> t_99 = 31/4 + (99 - 1) xx 7/4`
= `31/4 + 98 xx 7/4`
= `31/4 + 686/4`
= `717/4`
= `179 1/4`
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