The third term of an arithmetic sequence is-5 and the six terms is 7.what is the sum of the first 10 terms?
Answer (1)
Answer:To find the sum of the first 10 terms of the arithmetic sequence, follow these steps:1. **Find the common difference (d):** We know: - The third term (a3) is -5 - The sixth term (a6) is 7 The general formula for the nth term of an arithmetic sequence is: an = a1 + (n - 1)d For the third term: a3 = a1 + 2d = -5 For the sixth term: a6 = a1 + 5d = 7 Subtract the first equation from the second to find d: (a1 + 5d) - (a1 + 2d) = 7 - (-5) 3d = 12 d = 42. **Find the first term (a1):** Substitute d back into the equation for the third term: a1 + 2d = -5 a1 + 2(4) = -5 a1 + 8 = -5 a1 = -133. **Find the sum of the first 10 terms (S10):** The sum of the first n terms of an arithmetic sequence is given by: Sn = n/2 × (2a1 + (n - 1)d) For the first 10 terms: S10 = 10/2 × (2(-13) + (10 - 1) × 4) S10 = 5 × (-26 + 36) S10 = 5 × 10 S10 = 50So, the sum of the first 10 terms is 50.
