Question

The 8th term of an arithmetic sequence is 12 and it's 12 th term is 8. What is the algebraic expression for this sequence

Answer 1

Answer:

-n+20 = 20-n

Step-by-step explanation:

8th term  = 12

12th term = 8

↓                 ↓

position       term

common differenc, d = term difference / position difference

                                = 12-8 / 8-12

                                = 4/-4

                                = -1

first term,f = 8th term-7d                         or   f = 12th term-11d

                = 12-(7x-1)                                       = 8-(11x-1)

                = 12- -7 = 12+7 = 19                        = 8+11 = 19

algebraic expression or nth term = dn+(f-d)

                                                   = -1n+(19--1)

                                                   = -n+(19+1)

                                                   = -n+20 = 20-n