find the common difference of an AP whose first term is100 and sum of whose first 6 term is 5 times the sum of next 6term
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Sum(1 to 6) = a + a + d + a + 2d + a + 3d + a + 4d + a + 5d
= 6a + 15d
= 600 + 15d
Sum from 7 to 12 terms
T7 = 100 + 6d
T12 = 100 + 11d
sum from T7 to T12 = 600 + (6 + 7 + 8 + 9 + 10 + 11)d
= 600 + 51d
given 600 + 15d = 5(600 + 51d)
120 + 3d = 600 + 51d
48d = – 480
d = – 10
= 6a + 15d
= 600 + 15d
Sum from 7 to 12 terms
T7 = 100 + 6d
T12 = 100 + 11d
sum from T7 to T12 = 600 + (6 + 7 + 8 + 9 + 10 + 11)d
= 600 + 51d
given 600 + 15d = 5(600 + 51d)
120 + 3d = 600 + 51d
48d = – 480
d = – 10
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