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IgorLugansk [536]
2 years ago
9

Find the 5th term of the GP is 48 and it 8th term is 384. find the first term and the common​

Mathematics
1 answer:
rewona [7]2 years ago
7 0

Answer:

\text{1st term} = 3\\\\\text{Common ratio} = 2

Step by step explanation:

\text{Given that,}\\\\\text{5th term} = ar^{5-1} = ar^4 = 48~~~~~~~~...(i)\\ \\\text{8th term} = ar^{8-1} = ar^7 = 384~~~~~~~...(ii)\\\\\text{1st term,}~ a = ?\\\\\text{Common ratio,}~ r = ?\\\\(ii) \div (i):\\\\~~~~~~\dfrac{ar^7}{ar^4}=\dfrac{384}{48}\\\\\implies r^{7-4} = 8\\\\\implies r^3 = 8\\\\\implies r^3 = 2^3\\\\\implies r =2\\\\\text{Substitute r = 2 in eq (i):}\\\\~~~~~~a\cdot 2^4 = 48\\\\\implies 16a  =48\\\\\implies a = \dfrac{48}{16}\\\\\implies a = 3\\

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