Find the general formula for the arithmetic sequence below. Without using a recursive formula, calculate the $30^{\(\th\)}$ term.

$\(\left\]\lbrace\)-9,-4,1,6,\(\ldots\[\right\]\rbrace\)$

Write a recursive formula for the geometric sequence $\(\left\]\lbrace\)18,6,2,\(\frac\)23,\(\ldots\[\right\]\rbrace\)$.

Find the $10^{\(\th\)}$ term of the geometric sequence in which $a_1=5$ and $r=2$.

Write a formula for the general or $n^{\(\th\)}$ term of the geometric sequence where $a_7=1458$ and $r=-3$.

a.Does the sequence { k/(k + 1) } converge? Why or why not?

Suppose the sequence { aₙ} is defined by the explicit formula aₙ = 1/n, for n=1, 2, 3, .....Write out the first five terms of the sequence.

Suppose the sequence { aₙ} is defined by the recurrence relation a₍ₙ₊₁₎ = n · aₙ , for n=1, 2, 3 ...., where a₁ = 1. Write out the first five terms of the sequence.

The terms of a sequence of partial sums are defined by Sₙ = ∑ⁿₖ₌₁ k² , for n=1, 2, 3, .....Evaluate the first four terms of the sequence.