In an AP T5:T10 = 1:2and T12 = 36. Find difference.
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3, 6, 9, 12, 15, 18, 21, 24, 27, 30...
'n'th term in ap = a + (n-1)d
Thus, here, 5th term = a+4d
10th term = a+9d
12th term = a+11d
Given, (a+4d) / (a+9d) = 1/2
or, 2a + 8d = a + 9d
or, a = d
Also given, 12th term ⇒ a + 11d = 36
or, 12d = 36 [as a=d is proved previously]
or, d = 3
Thus, a = 3
Therefore, the ap: 3, 6, 9, 12, 15, 18...
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