Question

determine the 10th term from the end of the AP 4 9 14 dash 254

Answer 1

AS (Arithmetic Sequence ) : 4 , 9 , 14 ...... 254


CD ( Common Difference ) : 14 - 9 = 9 - 4 = 5


Given that l ( Last term ) = 254





By using the formula,
$\bold{a_{n} = a + (n - 1)d } \\ \bold{ l \: = a + (l - 1)d}$



254 = 4 + ( n - 1 )5

254 - 4 = ( n - 1 ) 5

250 / 5 = n - 1

50 = n - 1

50 + 1 = n

51 = n


Therefore, number of terms are 51




So, 10 terms before 51th term will be 41th term.

= > 41th term = a + ( 41 - 1 )d


= > 41th term = 4 + ( 40 ) 5


= > 41th term = 4 + 200


= > 41th term = 204






Hence, the 10th term from the end of the sequence is 204