✏️GEOMETRIC SEQUENCE
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[tex]\Large\color{black}{{\underline{\bold{ Question}}}}[/tex]
14. the first term of a geometric sequence is 2 and the fifth term is 32 find the common ratio and the sum of the 5 term?
D. r = 2, Sn = 62
15. if the sum of reciprocals of the first five terms of a harmonic progression is 60 find the third term of the sequence.
a. 1/12
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[tex]\Large\color{red}{{\underline{\mathfrak {{꧁"Explanation"꧂ }}}}}[/tex]
Find a common ratio :
[tex]an = a1 {(r)}^{n - 1} \\ 32 = 2 {(r)}^{5 - 1} \\ \frac{32}{2} = \frac{ {\cancel2r}^{4} }{\cancel2} \\ \sqrt[4]{16} = \sqrt[4]{ {r}^{4} } \\ r = 2[/tex]
Find sum of tern:
[tex]Sn = \frac{a1(1 - {r}^{n}) }{1 - r} \\ Sn = \frac{2(1 - {2}^{5}) }{1 - 2} \\ Sn = \frac{2(1 - 32)}{ - 1} \\ Sn = \frac{2(31)}{ - 1} \\ Sn = \frac{62}{ - 1} \\Sn = 62[/tex]
Since the r is 2 and sum is 62
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