Question

a challenge question for all Pls solve it fast ap question

Answer 1

Answer:

Middle term = a113 = 551

Sum of terms to it's left = 36400

Sum of terms to it's right = 87024

Step-by-step explanation:

The numbers are 103, 107, 111, ...... , 999

Hence, a1 = 103, d = 4, an = 999

Since a + ( n - 1 ) d = an,

103 + ( n - 1 ) 4 = 999

4 ( n - 1 ) = 896

n - 1 = 224

n = 225

Middle term = ( 225 + 1 ) / 2= 226 / 2 = 113 th term

a113 = 103 + ( 113 - 1 ) 4 = 103 + 448 = 551

Sum of terms on left side of middle term = S112

S112 = [ 112 / 2 ] [ 103 + a112 ]

S112 = 56 [ 103 + 547 ] as a112 = a113 - d = 551 - 4 = 547

S112 = 56 × 650

S112 = 36400

Sum of terms on right side of a113 = Sn - S113

Since n = 225, answer:

S225 - S113

= [ 225 / 2 ] [ 103 + a225 ] - [ 113 / 2 ] [ 103 + a113 ]

= [ 225 / 2 ] [ 103 + 999 ] - [ 113 / 2 ] [ 103 + 551 ]

= [ 225 / 2 ] [ 1102 ] - [ 113 / 2 ] [ 654 ]

= 225 × 551 - 113 × 327

= 123975 - 36951

= 87024