Identify if the sequence is arithmetic, geometric or quadratic. Assuming the r-st item of each se

Identify if the sequence is arithmetic, geometric or quadratic.
Assuming the r-st item of each sequence is ${a}_{1}$, give an expression for ${a}_{i}$.
If the sequence is arithmetic or geometric, compute the sum of the first 10 terms in the sequence
$1;4;13;28;49;...$
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${a}_{1}=1+3=4$
${a}_{2}=4+9=13$
${a}_{3}=13+15=28$
${a}_{4}=28+21=49$
(first difference)

Second difference is $6$

Thus, this is a quadratic sequence. (a sequence in which the second difference between each consecutive term differ by the same amount)