Q. 134.5( 8 Votes )

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Answer :

Let the first term = a


and common difference = d


We know,


nth term of an AP, an = a + (n – 1)d


Given


9th term of an AP is equal to seven times the second term


a9 = 7a2


a + (9 – 1)d = 7(a + d)


a + 8d = 7a + 7d


d = 6a ……[1]


Also,


Twelfth term exceeds five times the third term by 2


a12 = 5a3 + 3


a + 11d = 5(a + 2d) + 2


a + 11d = 5a + 10d + 2


d – 4a = 2


6a – 4a = 2 [From 1]


2a = 2


a = 1


From [1],


d = 6a


= 6(1)


= 6


Hence, first term of AP is 1 and common difference is 6.


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