The 5th term of an arithmetic sequence is 50, and the 12th term is 22. Find the nth term.

Question

Answer 1

a₁ + 4d = 50; a₁ + 11d = 22; 7d = - 28; d = - 4; a₁ = 66; a_n = 66 + (n - 1)(- 4); a_n = 70 - 4n.

Answer 2

a5=50

a12=22

for an arithmetic sequence

an= a1 +d(n-1) for the nth term, where a1=1st term and d= the common difference

12-5=7

50-22= 28

28/7 = -4 = d = the common difference

a5 = 50= a1 -4(5-1) = a1 -16

a1 = 50+16 = 66

an = 66 - 4(n-1)

a12 = 66 -4(11) = 66-44 = 22

an= 66 -4(n-1)

an = 66 -4n+4

an = 70-4n