The 1st 3terms of an arithmetic progression are x, (3x +1) and (7x -4). Find
i. the value of x
ii. the 10th term
i. To find the value of x, we can use the formula for the nth term of an arithmetic progression:
nth term = a + (n-1)d
where a is the first term, d is the common difference, and n is the term number.
Given that the first term is x, the second term is 3x + 1, and the third term is 7x - 4, we can see that the common difference is:
(3x + 1) - x = (7x - 4) - (3x + 1)
2x + 1 = 4x - 3
2 = 2x
x = 1
So, the value of x is 1.
ii. Now that we know the value of x, we can find the common difference and then the 10th term.
The common difference is:
(3(1) + 1) - 1 = (7(1) - 4) - (3(1) + 1)
4 - 1 = 7 - 4
3 = 3
So, the common difference is 3.
Now we can find the 10th term using the formula:
10th term = x + (10-1)d
10th term = 1 + 9(3)
10th term = 1 + 27
10th term = 28
Therefore, the 10th term of the arithmetic progression is 28.