# math

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The 4th term of an AP is 3 times its first term and the 7 term exceeds the 3 term by 1.Find the 10 term of an AP.

• math -

4th term is 3 times 1st term ----> a+3d = 3a
2a = 3d
a = 3d/2

7th term exceeds the 3rd term by 1
a+6d > a+2d by 1
a+6d = a+2d + 1
4d = 1
d = 1/4
then a= (3/2)(1/4) = 3/8

10th term = a+9d = 3/8 + 9(1/4) = 21/8

check: a=3/8, d=1/4 or 2/8
3/8, 5/8, 7/8, 9/8, 1/8, 13/8, 15/8, 17/8,19/8,21/8 ....
is 10th term 21/8 ? , yes
is 4th term 3 times the fist ? is 9/8 three times 3/8 ? yes
is 7th term bigger than 3rd term by 1 ?
is 15/8 - 7/8 = 1 ? yes

all is good

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