# math

In an arithmetic sequence , the 9th term is twice the 3rd term and 15th term is 80. Find the common difference and the sum of the terms from from 9th to 15th is inclusive

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1. Just change your English to math, using the definitions you learned.
"the 9th term is twice the 3rd term" ---> a + 8d = 2(a + 2d)
a + 8d = 2a + 4d
a = 4d
"15th term is 80" ----> a + 14d = 80

4d + 14d = 80

take it from there.

Use your sum of terms formula for the last part of your question.
Take the sum of 15 terms and subtract the sum of 8 terms from that.

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Reiny
2. a + r (n-1)

a + 8 r = 2(a+2r) = 2 a +4 r
a + 14 r = 80

a + 14 r = 80
a - 4 r = 0
------------------- suubtract
18 r = 80
r = 4.44
a = 4 r = 17.78

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Damon

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