The 3rd term of arthmetic sequence is 3/4th of 6th term.and their sum is 60.find a,d and nth term.
a + 2 d = (3/4)[ a + 5d ]
and
2 a + 7 d = 60
------------------------
(1/4 a -7/4 d = 0
or
1 a - 7 d = 0
2 a + 7 d = 60
------------------- add
3 a = 60
a = 20
d = 20/7
an = 20 + (n-1)(20/7)
To find the values of a, d, and the nth term in the arithmetic sequence, we can follow these steps:
1. Let's assume that the first term of the arithmetic sequence is 'a' and the common difference is 'd'.
2. We are given that the 3rd term is 3/4th of the 6th term.
So, the 3rd term can be written as: a + 2d (since the difference between the 1st and 3rd term is 2d).
And the 6th term can be written as: a + 5d (since the difference between the 1st and 6th term is 5d).
Therefore, we have the equation: a + 2d = (3/4)(a + 5d).
3. We are also given that the sum of all the terms in the arithmetic sequence is 60.
The sum of an arithmetic sequence is given by the formula: Sn = (n/2)(2a + (n-1)d), where Sn is the sum of the first n terms.
So, we have the equation: (n/2)(2a + (n-1)d) = 60.
4. Now, we have two equations:
a + 2d = (3/4)(a + 5d) ---(Equation 1)
(n/2)(2a + (n-1)d) = 60 ---(Equation 2)
To solve these equations and find the values of a, d, and the nth term, we need a third equation. Do you have any more information or conditions provided?