8 A geometric sequence has all positive terms. The sum of the first two terms is 15 and the sum to infinity is 27. a Find the value of the common ratio. b Hence, find the first term. 9 The first three terms of an infinite geometric sequence are m - 1, 6, m + 8. a Write down two expressions for r. bi Find two possible values of m. ii Hence, find two possible values of r. c i Only one of these r values forms a geometric sequence where an infinite sum can be found. Justify your choice for r. ii Hence, calculate the sum to infinity.
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a) From the given information, we know that the sum of the first two terms is 15, so we can write the equation a + ar = 15. We also know that the sum to infinity is 27. The formula for the sum to infinity of a geometric sequence is a / (1 - r), so we can write Show more…
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