# Mathematics

The first term of an Arithmetic Progression is -4 and the 15th term is double the 5th.
Find the 12th term of the AP

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"first term of an Arithmetic Progression is -4"
--> a=-4

"the 15th term is double the 5th" ---> a+14d = 2(a+4d)
a + 14d = 2a + 8d
6d = a
6d = -4
d = -2/3

term 12 = a + 11d
= -4 + 11(-2/3)
= -25/3

check: is the 15th term twice the 5th ??
term 15 = -4+14(-2/3) = -40/3
term 5 = -4 + 4(-2/3) = -20/3
YES

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2. -4+11(-2/3) will not give 25/3 but 34/3. Check that.

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