Question

Find middle term of the sequence formed by all 3-digit nos. which leave a remainder 3, when divided by 4. Also Find the sum of all the number on both sides of the middle term seprately.


plzzz its urgent:)

Answer 1

The list of 3 digit number that leaves a remainder of 3 when divided by 4 is :

103 , 107 , 111 , 115 , .... 999

The above list is in AP with first term, a = 103 and common difference, d = 4

Let n be the number of terms in the AP.

Now, an = 999

103 + ( n - 1 ) 4 = 999

103 + 4n - 4 = 999



4n + 99 = 999

4n = 900

n = 225

Since, the number of terms is odd, so there will be only one middle term.

middle term =
(
n+1
2
)
th
term =
113
th
term