Notes: ``5th term:` a_2 = 2, a_3 = -sqrt(2)` Find the indicated term of the geometric sequence.

Friday, August 2, 2013

5th term: $\displaystyle{a}_{{2}}={2},{a}_{{3}}=-\sqrt{{{2}}}$ Find the indicated term of the geometric sequence.

You need to write the following formula such that:

$\displaystyle{a}_{{5}}={a}_{{1}}\cdot{{q}}^{{4}}$

You need to evaluate q and $\displaystyle{a}_{{1}}$ , such that:

$\displaystyle{a}_{{3}}={a}_{{2}}\cdot{q}\Rightarrow{q}=\frac{{{a}_{{3}}}}{{{a}_{{2}}}}\Rightarrow{q}=\frac{{-\sqrt{{2}}}}{{2}}$

$\displaystyle{a}_{{2}}={a}_{{1}}\cdot{q}\Rightarrow{a}_{{1}}=\frac{{{a}_{{2}}}}{{q}}\Rightarrow{a}_{{1}}=\frac{{2}}{{\frac{{-\sqrt{{2}}}}{{2}}}}\Rightarrow{a}_{{1}}=-{2}\cdot\sqrt{{2}}$

You may evaluate $\displaystyle{a}_{{5}}={a}_{{1}}\cdot{{q}}^{{4}}$ such that:

$\displaystyle{a}_{{5}}=-{2}\cdot\sqrt{{2}}\cdot{{\left(\frac{{-\sqrt{{2}}}}{{2}}\right)}}^{{4}}$

$\displaystyle{a}_{{5}}=-{2}\cdot\sqrt{{2}}\cdot{\left(\frac{{4}}{{16}}\right)}\Rightarrow{a}_{{5}}=-\frac{\sqrt{{2}}}{{2}}$

Hence, evaluating $\displaystyle{a}_{{5}}$ yields $\displaystyle{a}_{{5}}=-\frac{\sqrt{{2}}}{{2}}.$

Notes

Friday, August 2, 2013

5th term: $\displaystyle{a}_{{2}}={2},{a}_{{3}}=-\sqrt{{{2}}}$ Find the indicated term of the geometric sequence.

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How does the choice of details set the tone of the sermon?

Friday, August 2, 2013

5th term: Find the indicated term of the geometric sequence.

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How does the choice of details set the tone of the sermon?

5th term: $\displaystyle{a}_{{2}}={2},{a}_{{3}}=-\sqrt{{{2}}}$ Find the indicated term of the geometric sequence.