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If the first term of a sequence is 8 and the 10th term is 53 what is the common difference?
Oz0tzotw8078
I am assuming this is an arithmetic series.
Use the formula nth term = a + (n-1)d where a is the 1st term, and d is the difference between each term.
10th term = 8 + (10-1)d
==>8 +9d=53
==> 9d = 53-8 = 45
==> d = 5
The difference is 5.
Wiki User
∙ 8y ago
Wiki User
∙ 8y agoYou have a(n) = a0 + n*d. With n = 1, we have a(1) = 8, and with n=10 we have a(10) = 53, so we have two equations, and two unknowns:
8 = a0 + 1*d ; 53 = a0 + 10*d. Take the first equation: rearrange so that a0 = 8 - d. Plug this into the other one: 53 = (8 - d) + 10*d. So 53 = 8 + 9*d, then solve for d:
53 - 8 = 9*d. 45 = 9*d. d = 5. Lets test it:
8, 13, 18, 23, 28, 33, 38, 43, 48, 53. Yes the 10th number is 53.
Wiki User
∙ 8y agoThe common difference is 5.
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