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geometric sequence? math?
1.) Identify the 12th term of a geometric sequence where a1 = 8 and a6 = -8,192.
2.) Identify the 10th term of the geometric sequence 7, -35, 175 …
2 Answers
- Anonymous9 years agoFavorite Answer
1). nth term=ar^(n-1)
8=ar^(1-1)=a
-8192=ar^5=8*r^5;
r^5=-8192/8=1024
r=4
12th term=ar^11=8*4^11=33554432
2). a=7
ar=-35
r=-5
10th term=ar^9=7*(-5)^9=-13671875
- 9 years ago
a[1] = m * r^1 = 8
a[6] = m * r^6 = -8192
-8192 / 8 = (m * r^6) / (m * r)
-1024 = r^5
-4 = r
8 = m * r
8 = m * (-4)
-2 = m
a[n] = -2 * (-4)^n
a[12] = -2 * (-4)^12
a[12] = -2 * (16384)
a[12] = 32768
2)
a[1] = 7 = m * r
a[2] = -35 = m * r^2
a[3] = 175 = m * r^3
-35 / 7 = m * r^2 / (m * r)
-5 = r
7 = m * (-5)
(-7/5) = m
a[n] = (-7/5) * (-5)^n
a[10] = (-7/5) * (-5)^10
a[10] = 7 * (-5)^9
a[10] = 7 * (-1953125)
a[10] = -13671875