Question

Find the sum of all even integers between 101 and 999

Answer 1

all even integers between 101 to 999 are ; 102, 104, 106, 108, ...... 998

first of all, we should find number of even number between 101 to 999.

using formula, Tn = a + (n - 1)d

here, a = 102, Tn = 998 , d = 2

then, 998 = 102 + (n - 1) × 2

or, 998 - 102 = 2(n - 1)

or, 896/2 = n - 1

or, n = 449

now, sum of all even integers is given by , Sn = n/2 [ a + Tn]

= 449/2 [ 102 + 998]

= 449/2 [ 1100 ]

= 449 × 550

= 246,950

hence, sum of all even integers between 101 to 998 is 246,950

Answer 2

Answer:

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