An important question from ML Aggarwal in which we have asked to find the sum of all two digits natural numbers which are divisible by 4.
ML Aggarwal Avichal Publication Arithmetic Progression Chapter 9 question no 20 i
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The two digits numbers which are divisible by 4 are
12,16,20,……96 in AP.
Sn = n/2(2a+(n -1)d)
Here a = 12 , d = 4.
tn = a + (n – 1) d
96 = 12 + ( n – 1) 4
84 = ( n – 1) 4
n – 1 = 21
∴n = 22
S22 = (22/2) (2×12 + (22 -1)4)
S22 = 11×[ 24 + 84]
S22 = 11×[ 24 + 84]
∴S22 = 1188.
The two digits numbers which are divisible by 4 are
12,16,20,……96 in AP.
Sn = n/2(2a+(n -1)d)
Here a = 12 , d = 4.
tn = a + (n – 1) d
96 = 12 + ( n – 1) 4
84 = ( n – 1) 4
n – 1 = 21
∴n = 22
S22 = (22/2) (2×12 + (22 -1)4)
S22 = 11×[ 24 + 84]
S22 = 11×[ 24 + 84]
∴S22 = 1188.