Given that the 11th term of an arithmetic progression is 43 and the first term is 3 find;
The common difference
To find the common difference, we can use the formula for the n-th term of an arithmetic progression:
An = A1 + (n-1)d
Given that the 11th term (An) is 43 and the first term (A1) is 3, we can plug these values into the formula:
43 = 3 + (11-1)d
Simplifying, we have:
43 = 3 + 10d
Subtracting 3 from both sides, we have:
40 = 10d
Dividing both sides by 10, we find:
d = 4
So, the common difference of the arithmetic progression is 4.
To find the common difference in an arithmetic progression, we can use the formula:
nth term = first term + (n - 1) * common difference
Here, we are given the 11th term (nth term = 11) as 43, and the first term as 3.
43 = 3 + (11 - 1) * common difference
Simplifying the equation:
43 = 3 + 10 * common difference
Subtracting 3 from both sides:
40 = 10 * common difference
Finally, divide both sides by 10:
common difference = 4
Therefore, the common difference in the arithmetic progression is 4.
To find the common difference of an arithmetic progression, we can use the formula:
nth term = first term + (n-1) * common difference
In this case, we are given the 11th term as 43 and the first term as 3. Let's substitute these values into the formula:
43 = 3 + (11-1) * common difference
Simplifying this equation:
43 = 3 + 10 * common difference
43 = 3 + 10d (where d represents the common difference)
Now, let's isolate the common difference:
43 - 3 = 10d
40 = 10d
Dividing both sides of the equation by 10:
40/10 = d
d = 4
Therefore, the common difference is 4.