Find the sum of the terms in the arithmetic series 50 + 57 + 64 + .. - HSC - SSCE Mathematics Advanced - Question 12 - 2024 - Paper 1

The nth term of an arithmetic series can be calculated using the formula:

$T_n = a + (n - 1)d$

Here, we know that the last term, $T_n$, is 2024, so we can set up the equation:

$2024 = 50 + (n - 1) imes 7$

Now, we can simplify this equation:

$2024 - 50 = (n - 1) imes 7$ $1974 = (n - 1) imes 7$ $n - 1 = \frac{1974}{7}$

Calculating the right-hand side, we get:

$n - 1 = 282$

So, adding 1 gives:

$n = 283$

The sum of the first n terms of an arithmetic series can be calculated using the formula:

$S_n = \frac{n}{2}(a + T_n)$

Substituting the known values into the formula gives:

$S_{283} = \frac{283}{2}(50 + 2024)$

Calculating this, we have:

$S_{283} = \frac{283}{2} imes 2074$

After performing the multiplication, we find:

$S_{283} = 293471$