Find the 1st term, d, and the 5th term of an arithmetic sequence whose 3rd term is 35 and whose 10th term is 77
Answer (1)
Answer:The 1st term (a₁) is 23, the common difference (d) is 6, and the 5th term (a₅) is 47.Step-by-step explanation:Arithmetic SequenceGiven:- 3rd term (a₃) = 35- 10th term (a₁₀) = 77 Solution1. Find the common difference (d):a₁₀ = a₃ + (10 - 3)d77 = 35 + 7d77 - 35 = 7d42 = 7dd = 42/7d = 62. Find the 1st term (a₁):a₃ = a₁ + (3 - 1)d35 = a₁ + 2(6)35 = a₁ + 12a₁ = 35 - 12a₁ = 233. Find the 5th term (a₅):a₅ = a₁ + (5 - 1)da₅ = 23 + 4(6)a₅ = 23 + 24a₅ = 47
