Calculate the sum of the arithmetic series 4 + 10 + 16 + .. - HSC - SSCE Mathematics Advanced - Question 12 - 2020 - Paper 1

The last term of the series is given as 1354. We can use the formula for the nth term of an arithmetic series:

$a_n = a + (n-1) d$ So, set 1354 = 4 + (n - 1) * 6.

Solving for n:

$1354 - 4 = (n - 1) * 6$ $1350 = (n - 1) * 6$ $n - 1 = \frac{1350}{6}$ $n - 1 = 225$ $n = 226$

We can use the formula for the sum of an arithmetic series:

$S_n = \frac{n}{2} (a + l)$ where (l) is the last term.

In this case:

$S_{226} = \frac{226}{2} \times (4 + 1354)$ $= 113 \times 1358$ $= 153454$