The 4th term of an A.P. is 13 while the 10th term is 31. Find the 24th term.

A.
89 
B.
75 
C.
73 
D.
69
Correct Answer: Option C
Explanation
a + 3d = 13 ………. (1)
a + 9d = 31 ………. (2)
(2) – (1): 6d = 18
d = 18/6 = 3
From (1), a + 3(3) = 13
a + 9 = 13
a = 13 – 9 = 4
Hence,
T_{24} = a + 23d
T_{24} = 4 + 23(3)
T_{24} = 4 + 69
T_{24} = 73
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