<s>[INST] Sequence and equation I am having a problem finding an equation for this sequence: 2, 2+4 , 2+4+6, 2+4+6+8 . 
Can someone show me the steps in solving this? 
 [/INST] We have $a_1 = 2 \times 1$, $a_2 = 2 \times 1 + 2 \times 2$, $a_3 = 2 \times 1 + 2 \times 2 + 2 \times 3$.
In general, we have
$$a_n = 2 \times 1 + 2 \times 2 + 2 \times 3 + \cdots + 2 \times n = 2 \times (1+2+\cdots+n) = 2 \times\dfrac{n(n+1)}2 = n(n+1)$$
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