Given that an arithmetic sequence has a common difference of 5 and sum of the first 10 terms is 245, the first term is?

The first term is 2.

2+7+12+17+22+27+32+37+42+47 = 245

To find the first term of an arithmetic sequence, we need to use the formula for the sum of the first n terms of an arithmetic sequence.

The formula for the sum of the first n terms of an arithmetic sequence is:
Sn = (n/2)(2a + (n-1)d)

Where:
Sn is the sum of the first n terms
a is the first term
d is the common difference
n is the number of terms

In this case, we are given that the common difference (d) is 5, and the sum of the first 10 terms (Sn) is 245.

So, we can plug in these values into the formula and solve for the first term (a).

245 = (10/2)(2a + (10-1)5)

Simplifying this equation:

245 = 5(2a + 9(5))

245 = 5(2a + 45)

Dividing both sides by 5 to isolate the expression inside the parentheses:

49 = 2a + 45

Subtracting 45 from both sides:

4 = 2a

Dividing both sides by 2:

2 = a

Therefore, the first term of the arithmetic sequence is 2.