The sum of the 8th and the 9th terms of an arithmetic sequence is 40 .
a) What is the sum of the first and the 16th terms of this sequence ?
b) What is the sum of the first 16 terms of this sequence ?
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Answer:
a) 40
b) 320
Step-by-step explanation:
a8 + a9 = 40
a + 7d + a + 8d = 40
2a + 15 d = 40
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a) a = 40 - 15d/2
a + a16 = (40 - 15d/2) + (40 - 15d/2) + 15 d
= 40 - 15d/2 + 40 - 15d/2 + 15d
= 40 - 15d + 15d
= 40
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b) n = 16
a = 40-15d/2
a16 = 40-15d/2 + 15d
s16 = 16/2 [40-15d/2 + (40-15d/2 + 15d)]
= 8 (40-15d/2 + 40 - 15d/2 + 15d)
= 8(40)
= 320
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