Question

find the number of terms in A.P. -9,-14,-19,-24...........-504

Answer 1

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Answer 2

Here is your solution :

Given,

First term ( a ) = -9

Last term ( l ) = -504

Common terms ( d ) = ?

Number of terms ( n ) = ?

To find the number of terms , firstly we have to find the common difference.

Using formula ,

=> Common difference = Difference of two consecutive terms

=> d = ( -14 ) - ( -9 )

=> d = -14 + 9

•°• d = -5

Now,

Using formula ,

=> Last term ( l ) = First term + ( No. of terms - 1 ) Common difference

=> -504 = -9 + ( n - 1 ) ( -5 )

=> -504 = -9 - 5n + 5

=> -504 = -4 - 5n

=> -504 + 4 = -5n

=> -500 = -5n

=> 5n = 500

=> n = 500 ÷ 5

•°• n = 100

Hence, this A.P. is having 100 terms.

Hope it helps !! ^_^