The 6th term of an AP is 37 and the 15th term is 91. Find d, a and the 25th term.
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
The th term of an AP is and the th term is . Find , and the th term.
Need a reminder? The key ideaShow
With two terms given, subtract them to find (the number of steps is the difference of the term numbers), then find . Three numbers in an AP: , , , with sum . To count numbers of a kind, find the first and the last and solve for .
The worked solution
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Step 1. The difference. , so .
Step 2. The first term. gives .
Step 3. The 25th term. .
Answer: , and the th term is .
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