Practice question · Numerical answer
Find the sum of the first 30 terms of the arithmetic sequence 2, 5, 8, 11, ...
Hints
- First find the thirtieth term, then use S_n = (n/2)(a_1 + a_n).
- a_30 = 2 + 29 x 3 = 89, and the average of 2 and 89 is 45.5.
Show the answer
1365
Why
a_30 = 2 + 29(3) = 89, so S_30 = (30/2)(2 + 89) = 15 x 91 = 1365. The formula says the sum is the number of terms times the average of the first and last. Gauss's pairing trick, and a much safer route than adding thirty numbers.
Practise Arithmetic and Geometric Sequences
The app has 7 more questions on this lesson, and keeps your place in the course. Mathematics I is free to start.
More questions on Arithmetic and Geometric Sequences
- A rumour spreads by each person telling two others; a savings account adds a fixed £50 a month. Why is the…
- An arithmetic sequence adds a fixed amount each step; a geometric one multiplies by a fixed factor. Why does…
- Order the steps of finding the sum 3 + 6 + 12 + ... + 384.
- An arithmetic sequence has first term 4 and common difference 7. Find the twentieth term.
- A geometric sequence has first term 5 and common ratio 3. Find the sixth term.