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Chapter 11: Problem 35

Find the sum of the first 20 terms of the arithmetic sequence: \(4,10,16,22, \dots\)

Short Answer

Expert verified
The sum of the first 20 terms of the given arithmetic sequence is 1220.

Step by step solution

01

Identify the first term (a) and common difference (d)

Upon observation, it can be seen that the first term, 'a' is 4. The common difference 'd', difference between any two consecutive terms, is 10 - 4 = 6.
02

Find the 20th term

The nth term of an arithmetic sequence is given by \(a + (n-1)d\). Here, n = 20, a = 4, d = 6. Substituting these values in the formula, we get the 20th term, \(l = 4 + (20-1)*6 = 118.
03

Compute the sum of the first 20 terms

As mentioned earlier, we can use the formula for the sum of an arithmetic progression \(S_n = \frac{n}{2} (a + l)\). Substituting n = 20, a = 4 and l = 118, we get \(S_{20} = \frac{20}{2} * (4 + 118) = 10 * 122 = 1220.\)

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