If the nth term is 99 of the given A.P. ,then find the value of n if the first term is 7 and common difference is 2.
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If the nth term is 99 of the given A.P. ,then find the value of n if the first term is 7 and common difference is 2.
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Solution:-
Given:-
=> First term ( a ) = 7
=> Common difference ( d ) = 2
=> Tₙ = 99
To find
=> Number of terms ( n )
Formula
=> Tₙ = a + ( n - 1 )d
Now putting the value on formula
=> 99 = 7 + ( n - 1 ) × 2
=> 99 = 7 + 2n - 2
=> 99 = 5 + 2n
=> 99 - 5 = 2n
=> 94 = 2n
=> 94 / 2 = n
=> n = 47
So number of term ( n ) = 47
Now checking our answer
=> 99 = 7 + ( n - 1 ) × 2
=> 99 = 7 + ( 47 - 1 ) × 2
=> 99 = 7 + 46 × 2
=> 99 = 92 + 7
=> 99 = 99
LHS = RHS
[tex]{\bold{\blue{\boxed{\bf{Given}}}}}[/tex]
[tex]{\bold{\blue{\boxed{\bf{To\:find}}}}}[/tex]
[tex]{\bold{\blue{\boxed{\bf{ Formulae\:used }}}}}[/tex]
[tex]\bold a_n = a + (n-1)d [/tex]
[tex]{\bold{\blue{\boxed{\bf{ Solution }}}}}[/tex]
[tex] 99 = 7 + (n -1)\times 2[/tex]
[tex] 99 - 7 = ( n - 1 ) 2 [/tex]
[tex] 92 = ( n - 1 ) 2 [/tex]
[tex] n - 1 = \dfrac{92}{2} [/tex]
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[tex] n - 1 = 46 [/tex]
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[tex] n = 46 + 1 [/tex]
⠀⠀⠀⠀
[tex] n = 47 [/tex]
[tex]{\bold{\blue{\boxed{\boxed{\bf{n = 47}}}}}}[/tex]