For every positive integer n, the sum of the first n terms of a sequence is Sn = 3n² + 5n…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
For every positive integer , the sum of the first terms of a sequence is .
- What is the first term?
- Show that the sequence is an arithmetic progression. What is its common difference?
- What is the 15th term?
- Which term of the sequence is 152?
- What is the sum of the 11th to the 20th terms, both included?
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.
Plan. Get the th term from the sums, then answer every part from it.
(a) .
(b) For , . This also gives , so the formula holds for every . It is linear in , so each term is more than the one before: an AP with common difference .
(c) .
(d) gives : the th term.
(e) .
Check. Writing out the first forty terms from the sums and adding the 11th to the 20th one by one gives the same 950, and every difference between neighbours is 6.
Watch out. is not the th term. is the sum of fifteen terms, not the 15th term.
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