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To find the first term and common ratio of a geometric progression, we can use the formula for the nth term of a geometric sequence: (a_n = a_1 \times r^{(n-1)}). Given that the 6th term is 160 and the 9th term is 1280, we can set up two equations using these values. From the 6th term, we get (a_1 \times r^5 = 160), and from the 9th term, we get (a_1 \times r^8 = 1280). By dividing the two equations, we can eliminate (a_1) and solve for the common ratio (r).

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βˆ™ 5d ago
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βˆ™ 10y ago

ar5 = 160

ar8 = 1280

so r3 = 1280/160 = 8 and so r = 2

then, ar5 = 160 gives a = 160/32 = 5

First term = a = 5

Common ratio = r = 2

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Q: What will be the first term and the common ratio of geometric progression whose 6th and 9th terms are 160 and 1280 respectively?
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