# Math

The sixth term of an A.P. is 5 times the first term and the eleventh term exceeds twice the fifth term by 3 . Find the 8th term ?

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1. a+5d = 5a
a+10d = 2(a+4d)+3

Now you can find a and d, and then a+7d.

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2. translate the English into Math...
"The sixth term of an A.P. is 5 times the first term"
---> a+ 5d = 5a or 5d = 4a
a = 5d/4

"eleventh term exceeds twice the fifth term by 3"
term(11) -2 term(5) = 3
a + 10d - 2(a + 4d) = 3
-a + 2d = 3
-5d/4 + 2d = 3
times 4
-5d + 8d = 12
d = 4
then a = (5/4)(4) = 5

check:
term6 = a + 5d = 25 which is 5 times the first term
term 11 = a+10d = 45
twice term5 = 2(21) = 42 , which is 3 less than term11

term8 = a + 7d = 5 + 28 = 33

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3. tikka

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