The 1st 3terms of an arithmetic progression are x, (3x +1) and (7x -4). Find

Question

i. the value of x
ii. the 10th term

Answer 1

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.