Find the sum off all multiple of 7 lying between 100and 1000
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It is a question of arithmetic progression
105,112,.....994
First term = a = 105
Last term = tn = 994
Common difference = d = 7
By formula
tn = a+ (n-1)d
994 = 105 + (n-1)7
994-105 = 7n - 7
889 = 7n - 7
889 + 7 = 7n
896 = 7n
896/7 = n
128 = n
By formula
Sn = n/2(2a + (n-1)d)
Sn = 128/2(2*105 + (128-1)7)
Sn = 64(210+127*7)
Sn = 64(210+889)
Sn = 64 * 1099
Sn = 70336
It's a big calculation but practice A.P much then it would be a lot easier
105,112,.....994
First term = a = 105
Last term = tn = 994
Common difference = d = 7
By formula
tn = a+ (n-1)d
994 = 105 + (n-1)7
994-105 = 7n - 7
889 = 7n - 7
889 + 7 = 7n
896 = 7n
896/7 = n
128 = n
By formula
Sn = n/2(2a + (n-1)d)
Sn = 128/2(2*105 + (128-1)7)
Sn = 64(210+127*7)
Sn = 64(210+889)
Sn = 64 * 1099
Sn = 70336
It's a big calculation but practice A.P much then it would be a lot easier
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