SOLUTION: Two elements of a sequence are 3 and 13. (a) Write down the first few terms of at least four sequences having 3 and 13 as two of its elements. (b) Find the 25th element in each o

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Question 1045000: Two elements of a sequence are 3 and 13.
(a) Write down the first few terms of at least four sequences having 3 and 13 as two of its elements.
(b) Find the 25th element in each of your sequences.
(c) Find the general term of each of your sequences if you can.
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
(I) 3, 13, 23, 43, 53, 63, ...

That's the arithmetic sequence that has first term a1=3
and common difference d=10.  So we use the formula for the nth
term:

an = a1+(n-1)d

Substituting a1=3, d=10.

The general term is

an = 3+(n-1)(10)

an = 3+10(n-1)

an = 3+10n-10

an = 10n-7    <--general term

Substituting n=25

a25 = 10(25)-7

a25 = 250-7

a25 = 243     <--25th element

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(II) 3, 8, 13, 18, 23, 27, ...

That's the arithmetic sequence that has first term a1=3
and common difference d=5.  

Do it the same way.

-------------------------

(III) 1, 3, 5, 7, 9, 11, 13, 15, ...

That's the arithmetic sequence that has first term a1=1
and common difference d=2.  

Do it the same way.

Edwin