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What is the 55th term of a sequence if the 6th term is 4 and the 100th term is 98?

 Jun 25, 2015

Best Answer 

 #2
avatar+26396 
+13

What is the 55th term of a sequence if the 6th term is 4 and the 100th term is 98 ?

 

an=a1rn1a6=a1r5=4a100=a1r99=98a100a6=a1r99a1r5=984a1r99a1r5=984r99r5=24.5r995=24.5r94=24.5r=9424.5r=1.03461402806a6=a1r5=4a1r5=4a1=4r5a1=41.034614028065a1=3.37417946747a55=a1r54a55=3.374179467471.0346140280654a55=21.1933572378

 

 Jun 25, 2015
 #1
avatar+33654 
+5

If this is an arithmetic sequence then the n'th term is a + (n-1)d where a is the first and d is the difference.

a + 5d = 4

a + 99d = 98

 

so a = -1 and d = 1

the 55th term is -1 + 54*1 = 53

.

 

If this is a geometric sequence then the n'th term is a*rn-1 where r is the multiplier.

 

a*r5 = 4

a*r99 = 98

 

r=(98/4)1/94 ≈ 1.0346

a = 4/1.03465 ≈ 3.3742

 

The 55th term is 3.3742*1.034654 ≈ 29.193

 

.

 Jun 25, 2015
 #2
avatar+26396 
+13
Best Answer

What is the 55th term of a sequence if the 6th term is 4 and the 100th term is 98 ?

 

an=a1rn1a6=a1r5=4a100=a1r99=98a100a6=a1r99a1r5=984a1r99a1r5=984r99r5=24.5r995=24.5r94=24.5r=9424.5r=1.03461402806a6=a1r5=4a1r5=4a1=4r5a1=41.034614028065a1=3.37417946747a55=a1r54a55=3.374179467471.0346140280654a55=21.1933572378

 

heureka Jun 25, 2015

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