Problem 35
Question
Find the sum of the first 20 terms of the arithmetic sequence: \(4,10,16,22, \dots\)
Step-by-Step Solution
Verified Answer
The sum of the first 20 terms of the given arithmetic sequence is 1220.
1Step 1: 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.
2Step 2: 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.
3Step 3: 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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Problem 35
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