The ninth term of an ap is equal to seven times the second term and twelfth terms exceeds five times the third term by 2.Find the first term and common difference
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a 9 = 7 ( a2)
a + 8d = 7 ( a + d )
a + 8d = 7a + 7d
8d - 7d = 7a - a
d. = 6a
Case II ..
a + 11d + 2 = 5 ( a + 2 d )
a + 11d +2 = 5 a + 10 d
11d - 10d + 2 = 5a - a
d + 2 = 4a
6a - 4a = -2
2a = -2
a = -1
so , d = 6a
d = -6
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a 9 = 7 ( a2)
a + 8d = 7 ( a + d )
a + 8d = 7a + 7d
8d - 7d = 7a - a
d. = 6a
Case II ..
a + 11d + 2 = 5 ( a + 2 d )
a + 11d +2 = 5 a + 10 d
11d - 10d + 2 = 5a - a
d + 2 = 4a
6a - 4a = -2
2a = -2
a = -1
so , d = 6a
d = -6
HOPE IT HELPS YOU! !
AND FOLLOW ME !!!
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