Question

5,15,25,35,45,..., Determine if the given sequences represent an AP, assuming that the pattern continues. If it is an AP, find the nth term.

Answer 1

use formula, dₙ = $a_{n+1}-a_n$

In the above sequence,
a = 5;
d₁ = a₂ –a₁ = 15–5 = 10
d₂ = a₃ –a₂  = 25–15 = 10
d₃ = a₄ –a₃  = 35–25 = 10

⇒ As in A.P the difference between the two terms is always constant. The difference in sequence is same and comes to be 10.
∴ The above sequence is A.P
The nth term of A.P is aₙ = a + (n–1)d
aₙ = a + (n–1)d = 5 + (n–1)10
= 5 + 10n–10
= –5 + 10n

Answer 2

Hi ,

A sequence of numbers in which the

successive terms increase or decrease

by a constant number is called an

Arithmetic Progression ( A.P )

Here ,

Given sequence is 5 , 15 , 25 ,35 , 45 ,...

a2 - a1 = 15 - 5 = 10

a3 - a2 = 25 - 15 = 10

a4 - a3 = 35 - 25 = 10

Therefore ,

a2 - a1 = a3 - a2 = a4 - a3 = ... = d = 5

common difference = ( d ) = 5

Given sequence is in A.P.

nth term of A.P = an

an = a + ( n - 1 )d [ here first term = a ]

= 5 + ( n - 1 ) 10

= 5 + 10n - 10

an = 10n - 5

I hope this helps you.

: )