Csdrhrt

So I am a High School Student and I take advanced Mathematics but this was in the core paper. I was told I was not allowed to use anything that we haven't been taught in core(Calculus)

This is the question

$x_0$ (row 1): 2

$x_1$ (row 2): 6; 10

$x_2$ (row 3): 14; 18; 22

$x_3$ (row 4): 26; 30; 34; 38

$x_4$ (row 5): 32....

What is the sum of the numbers(ie 100 + 101 = 201) in the 8th row.

I think the row is

$$x_{n+1} = x_n + 4 $$
where $x_0 = 2 $

I can do this question using calculus

My method:

$r= a.row.you.want - 1$

$g = frac{(r^2)}{2} + frac{(r)}{2}$

$$sum_{n=g}^{g+r} 4n+2$$

$r = 7$

$g = frac{(7^2)}{2} + frac{(7)}{2}$
$;g = 28$

$$sum_{n=28}^{35} 4n+2 =1024$$

But since it was in core there must be a function that can do this without the need for sigma.

Can anyone help?

Alternative method.

Firstly, the numbers $2,6,10,14,...$ form an arithmetic progression $a_n$ with $a_1=2,d=4$.

Secondly, notice the correspondence between the row number and the number of terms, so the row $8$ will have $8$ terms.

Thirdly, notice the first terms in each row: $a_1,a_2,a_4,a_7,a_{11},a_{16},a_{22},a_{29}$...

Hence, you add the row $8$ terms:
$$a_{29}+a_{30}+cdots +a_{36}=frac{a_{29}+a_{36}}{2}cdot 8=frac{a_1+28d+a_1+35d}{2}cdot 8=1024.$$