Math, asked by sparida4848, 1 year ago

How do you find the first five terms in the geometric sequence which is such that the sum of the 1st and 3rd terms is 50, and the sum of the 2nd and 4th terms is 150?

Answers

Answered by kartik2507
0

a + ar^2 = 50 (1)

ar + ar^3 = 150 (2)

divide (2) by (1)

 \frac{ar + a {r}^{3} }{a +  {ar}^{2} }  =  \frac{150}{50}  \\   \frac{ar(1 +  {r}^{2} )}{a(1 +  {r}^{2}) }  =  \frac{150}{50}  \\ r = 3 \\ substitute \: r \: in \: (1) \\ a + a {r}^{2}  = 50 \\ a(1 +  {r}^{2} ) = 50 \\ a(1 + 9) = 50 \\ a \times 10 = 50 \\ a =  \frac{50}{10}  = 5 \\ the \: terms \: are \\ a \: ar \: a {r}^{2}  \: a {r}^{3}  \: a {r}^{4}  \\ 5 \:  \: 15 \: \:  45 \: \:  135 \:  \: 405

5, 15, 45, 135, 405

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