If the sum of the first five terms of an Arithmetic sequence is equal to 120 and the sum of the next five terms of the same Arithmetic Sequence is equal to 245, what is the 4th term of this Sequence?
A) 29
B) 34
C) 81
D) 86
E) 91
Answer: A
Source: e-GMAT
If the sum of the first five terms of an Arithmetic sequence is equal to 120 and the sum of the next five terms of the
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Solution:
We can let the first term = x and the common difference = d. Thus, the second term = x + d, the third term = x + 2d, and so on. We can create the equations:
x + (x + d) + (x + 2d) + (x + 3d) + (x + 4d) = 120 → 5x + 10d = 120
and
(x + 5d) + (x + 6d) + (x + 7d) + (x + 8d) + (x + 9d) = 245 → 5x + 35d = 245
Subtracting the first equation from the second equation, we have:
25d = 125
d = 5
Substituting d = 5 into the first equation, we have:
5x + 50 = 120
5x = 70
x = 14
Since the fourth term is x + 3d, the fourth term is 14 + 3(5) = 29.
Answer: A
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