find the difference between the sums of the first 50 terms of the arithmetic sequence 5, 8, 11... and 9, 12, 15...
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first sequence is 5,8,11....
n = 50
a = 5
d = 8-5 = 3
Sn = n/2 (2a+(n-1)d)
= 50/2 (2×5+(49)3)
= 25 (10+147)
= 25 (157)
= 3925
second sequence is 9,12,15...
n = 50
a = 9
d = 12-9=3
Sn = n/2 (2a+(n-1)d)
S50 = 25 (18+49×3)
S50 = 25 (18+147)
S50 = 25×165
S50 = 4125
difference between two sequence = 4125 - 3925
= 200
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