a challenge question for all Pls solve it fast ap question
Answers
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