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The sum of the first and last terms of a linear sequence is 42. If the sum of all the terms is 420 and the second term is 4, find .
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Use this formula for the sum of arithmetic progression:
= .
(see the lesson Arithmetic progressions in this site).
Then you get
= ---> n = 20.
Next, from the condition you have these two equations
+ = 42,
= ,
or
+ = ,
= ,
or
+ = ,
= .
The solution of this system is = 2, d = 2.
Get it by any method.
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Do not use the term "a linear sequence".
Use the commonly accepted term "arithmetic progression".