Question

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.​

Answer 1

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

Answer 2

${\bold{\blue{\boxed{\bf{Given}}}}}$

• first term = a = 7
• common diff. = d = 2
• nth term = 99

${\bold{\blue{\boxed{\bf{To\:find}}}}}$

• $\bold n = ???$

${\bold{\blue{\boxed{\bf{ Formulae\:used }}}}}$

$\bold a_n = a + (n-1)d$

${\bold{\blue{\boxed{\bf{ Solution }}}}}$

$99 = 7 + (n -1)\times 2$

$99 - 7 = ( n - 1 ) 2$

$92 = ( n - 1 ) 2$

$n - 1 = \dfrac{92}{2}$

⠀⠀⠀⠀

$n - 1 = 46$

⠀⠀

$n = 46 + 1$

⠀⠀⠀⠀

$n = 47$

${\bold{\blue{\boxed{\boxed{\bf{n = 47}}}}}}$