If X+6, 2x+1, 4x-13,... Form An Arithmetic Sequence Find The 5th Term. (Show Your Solution).

If x+6, 2x+1, 4x-13,... Form an arithmetic sequence find the 5th term. (Show your solution).

 

Answer:

The fifth term (a₅) is 31.

Step-by-step explanation:

Given:

a₁ = x+6

a₂ = 2x+1

a₃ = 4x-13

Find the value of x:

a₂ - a₁ = a₃ - a₂   ⇒  common difference formula

2x+1 - (x+6) = 4x-13 - (2x+1)

2x + 1 - x - 6 = 4x - 13 - 2x - 1

2x - x - 4x + 2x = -13 - 1 - 1 + 6

-x = -9

x = 9

The sequence:

a₁ = x+6 ⇒  9=6 = 15

a₂ = 2x+1  ⇒  2(9)+1 = 19

a₃ = 4x-13  ⇒  4(9)-13 = 23

The sequence is: 15, 19, 23

The common difference (d) is 4.

Find the 5th term:

n = 5

a₁ = 15

an = a₁ + (n-1)(d)  ⇒  General Rule

a₅ = 15 + (5-1)(4)

a₅ = 15 + 16

a₅ = 31

The fifth term (a₅) is 31.


Comments

Post a Comment

Popular posts from this blog

Kabanata 1 Mensahe Noli Me Tangere

Kabanata 1 mensahe noli me tangere   para sa akin ang mga mensahe na nais iparating ng kabanata 1 ng nobelang Noli Metangere Ang pag aaway nina Tenyente Guevarra (pamahalaan) at Padre Damaso (simbahan) ay nagpapakita na noong unang panahon ,ang pamahalaan at ang simbahan ay hindi nagkakaisa o nagkakasundo dahil sa ibig mangibabaw ang bawat isa. Isa pang mensahe na nakikita ko sa kabanatang ito ay ang pagiging mahiyain noon ng mga babae na nagpapakita na ang lalaki ay mas makapangyarihan sa mga babae. Sana ay makatulong i-click ang link para sa karagdagang kaalaman sa Noli Me tangere brainly.ph/question/2082362 brainly.ph/question/1652889 brainly.ph/question/302069
Read more

What Two Secrets About The Labyrinth Had Daedalus Kept From King Minos? And How Did Of These Secrets Help Them To Escape?

What two secrets about the Labyrinth had Daedalus kept from king Minos? And how did of these secrets help them to escape?   14 young people was annually being sent by Athens to Crete, to be killed by the Minotaur inside the labyrinth until the son of King Aegeus, Theseus, vowed to put an end to his people's suffering. As one of the tributes, he volunteered and left Athens in the ship hoisting the traditional black sails in mourning for the victims. He told his father that he would change the sails to white on the trip home, should he be successful. When Theseus arrived on crete, he attracted the attention of Ariadne, Minos' daughter, who fell in love with him and secretly gave him a sword and a ball of twine . She told him to attach the thread to the opening of the labyrinth so that after he had killed the Minotaur, he could then able to follow it back to escape. Theseus kills the monster, saves the youths who were with him inside the labyrinth, and escapes from Crete with...
Read more