Question

arithmetic sequence 10,14,18,.. it possible that the difference between any two terms 464? why?​

Answer 1

A.P : 10,14,18,..

• a = 10 d = 4

an = a+(n-1)d

an = 10+(n-1)4

an = 10+4n-4

an = 4n+6 ________(1)

Tn = a+(n-1)d

Tn = 10+(n-1)4

Tn = 10+4n-4

Tn = 4n+6 ________(2)

According to Question,

an + Tn = 4n+6 + 4n+6

464 = 8n+12

452 = 8n

n = 56.6

We know that ,

• Number of term in A.p Can't be in decimals.

So, it is not possible that the difference between any two terms is 464 of Given A.p

Answer 2

[tex]A.P : 10,14,18,..10,14,18,..a = 10 d = 4 d = 4an = a+(n-1)dn-1)dan = 10+(n-1)4-1)4an = 10+4n-4-4an = 4n+6 ________(1)________(1)Tn= a+(n-1)d________(1)Tn = a+(n-1)dTn =10+(n-1)410+(n-1)4Tn = 10+4n-4Tn = 4n+6 ________(2)________(2)According toQuestion,an + Tn = 4n+6 + 4n+6

an + Tn = 4n+6 + 4n+6464 = 8n+12

452 = 8nn = 56.6We know that , We know that , Number of term in A.p Can't be in decimals.We know that , Number of term in A.p Can't be in decimals.So, it is not possible that the difference between any two terms is 464 of Given A.ptwo terms is 464 of Given A.p[/tex]