Answered

Sumali sa IDNStudy.com at makakuha ng mga sagot sa iyong mga tanong. Sumali sa aming komunidad ng mga bihasa upang makahanap ng mga sagot na kailangan mo sa anumang paksa o problema.

what is the 20th term of an arithmetic sequence is given that its 4th term is 79 and its ninth term is 54?

Sagot :

4th term = 1st term + 3d = 79
9th term = 1st term + 8d = 54

9th term - 4th term 
54 - 79 = (1st term + 8d) - (1st term + 3d)
-25 = 1st term + 8d - 1st term - 3d
-25 = 5d
-5 = d

20th term
= 1st term + 19d
= 9th term + 11d
= 54 + 11(-5)
= 54 - 55
= -1


To find d, let the a₄= a₁.

an= a₁ + (n-1) d
54= 79 + (6-1) d      *6 since we started to count the terms in a₄*
54 = 79 + (5)d
54 - 79 = 5d            * Transpose; combine like terms*
-25= 5d                  * Divide both sides by 5*
   5

-5 = d

Find a₁:

an= a₁ + (n-1) d
54 = a₁ + (9-1) -5
54 = a₁ + (8) -5
54 = a₁ + (-40)
54 + 40 = a₁
94 = a₁

find a₂₀:

an= a₁ + (n-1) d
a₂₀ = 94 + (20 - 1) -5
     = 94 + (19) -5
     = 94 + (-95)
     = -1