Explain only..help?

Question

Write down an expression, in terms of n, for the nth term of the sequence 1, 7, 13, 19, 25, 31, ...

The answer is 6n - 5

I don't understand why it is -5. I know it's 6n as the term increases by 6 down the sequence..But why do you need to put a -5 at the back? Pls explain

Answer 1

the first term of your sequence corresponds to n=1.

so you have for n=1 the first term is 1= 6*1 + b
and the resolution of that equation gives you b=-5

so your sequence is 6n-5

Answer 2

okay this is pretty simple!

As per law, the nth of a sequence is given by:

(A)n = (A)1 + (n - 1)d
where (A)1 is the first term of the sequence and d is the common difference.

So in the case of your sequence:
(A)1 = 1
d = 5
so,

(A)n = 1 + (n-1)(6)
= 1 + 6n - 6
= 6n - 5

Got it!?
:)

Answer 3

This is an AP expression
using formula:
Tn=a+(n-1)d,
a=1
d=T2-T1=7-1=6

Tn=a+(n-1)d
=1+(n-1)(6)
=1+6n-6
=6n-5#

Answer 4

When n =1 6n=6
but your sequence starts at 1. You need the -5 to reset the starting point back to the 1 you actually started with.

Answer 5

Tn=a+(n-1)d
you are looking for Tn
so we found that a=1, d=6 only
Tn=1+(n-1)6
=1+6n-6
=6n-5
got it?
if u dun put da -5 in da formula...then u wouldnt get da answer...
because sometimes wat if they ask u 2 find da answer for da 90th number?...

Answer 6

6n is 6,12,18,24,30,36 and so on. 1,7,13,19,25,31 are 5 less for each term. That's why.