.
the sum of the first and last terms of an arithmetic progression is 42.the sum of all the terms is 420.
If the second term is 4, find the number of term,common difference,last term of the sequence
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
For any arithmetic progression, the half of the sum of its first and last terms, multiplied by the number of terms is equal to the sum of the terms.
Therefore, the number of the terms, based on given condition, is
n = = 20.
Further, we have
= 42, or = 42, or = 42, and
= = 4.
So, you have two equations for two unknowns
= 42,
= 4.
Solve it on your own by any method you know.
There is a bunch of lessons on arithmetic progressions in this site:
- Arithmetic progressions
- The proofs of the formulas for arithmetic progressions
- Problems on arithmetic progressions
- Word problems on arithmetic progressions
- Mathematical induction and arithmetic progressions
- One characteristic property of arithmetic progressions
- Solved problems on arithmetic progressions
Also, you have this free of charge online textbook in ALGEBRA-II in this site
- ALGEBRA-II - YOUR ONLINE TEXTBOOK.
The referred lessons are the part of this online textbook under the topic "Arithmetic progressions".