The sum of 4 consecutive terms which are in an ap is 32 and the ratio of the product of the first and the last term of the product of 2 middle terms is 7:15. Find the number
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a-3d+a-d+a+d+a+3d=32
4a=32
a=8
a2-9d2/a2-d2=7/15
128d2=512
d=+-4
4a=32
a=8
a2-9d2/a2-d2=7/15
128d2=512
d=+-4
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Answer:
Let the four consecutive term of the AP be ,
a - 3 d , a - d , a + d , a + 3 d
A.T.Q.
a - 3 d + a - d + a + d + a + 3 d = 32
4 a = 32
a = 8
and
( a - 3 d ) ( a + 3 d ) / ( a - d ) ( a + d ) = 7 / 15
15 ( a² - 9 d² ) = 7 ( a² - d² )
8 a² = 128 d² [ a = 8 ]
d = ± 2
Therefore , numbers are 2 , 6 , 10 , 14 or 14 , 10 , 6 , 2 .
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