Final answer:
To find the sum of the first 35 terms of an arithmetic sequence, we first determine the first term and the common difference using the given sums of the first 15 and 20 terms. Then we apply the arithmetic sequence sum formula to arrive at the sum of the first 35 terms. The answer is calculated as S35 = 35/2 (2a + 34d).
Step-by-step explanation:
The student is asking for the sum of the first 35 terms of an arithmetic sequence, given that the sum of the first 15 terms is 20 and that the sum of the first 20 terms is 15.
We can use the formula for the sum of n terms in an arithmetic sequence, which is Sn = n/2 (2a + (n-1)d) where a is the first term and d is the common difference. The sum of the first 15 terms (S15) is 20, so we have 20 = 15/2 (2a + 14d). Similarly, the sum of the first 20 terms (S20) is 15, so we have 15 = 20/2 (2a + 19d). Solving these two equations simultaneously, we find the values of a and d.
With a and d known, we can find the sum of the first 35 terms (S35) using the same formula. The answer is calculated as S35 = 35/2 (2a + 34d).