the seventh term of a n arithmetic progression is 4times it,2and 12term is 2more than 3times of its 4th term . find the progression
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The 7th term of an arithmetic progression is four times its second term and twelfth term is 2 more than three times of its fourth term.Find progression.
7th Term = a + 6d
2nd term = a + d
7th term = 4 * (2nd Term)
=> a + 6d = 4 (a + d)
=> a + 6d = 4a + 4d
=> 2d = 3a - eq 1
12th term = a + 11d
4th term = a + 3d
12th term = 2 + 3 * 4th term
a + 11d = 2 + 3 *(a + 3d)
=> a + 11d = 2 + 3a + 9d
=> 2d = 2a + 2 - eq2
Equating both equations
3a = 2a + 2
=> a = 2
2d =3a
=> 2d = 6
=> d= 3
AP = 2 + (n-1)3
= 2 + 3n - 3
= 3n - 1
2 , 5 , 8 , 11....
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