i need to find the nth shape for this patter 1,5,9,13,17, etc.?

Question

the problem begins with one cube, each time I add one cube to the 4 sides of the first cube. ex.shape 1 = 1 cube, shape 2 = 5 cubes, shape 3 = 9 cubes, and so on and so on. I need to figure out the nth shape

Answer 1

Look at the differences between adjacent elements...

Answer 2

basically it is an arithmetic progression

formula Nth term= a + (N-1) * (difference)

a is the first term
difference is the difference between the next term and the previous one



nth cube = 1+ (n-1)(4)
=1+4n-4
nth cube =4n-3
put values for n and find out answers for many values,
it'll be correct

Answer 3

Cubes in Nth shape = -3+4n

Answer 4

The nth shape will be the number of cubes before n and add 4 to it to get the nth shape

Answer 5

This is an A.P (Arithmetic Progression)
To find the nth shape of this pattern, use the formula
Tn = a + (n - 1)d
where,
a = 1(First number in A.P), d = T2 - T1 = 5-1=4.(Common difference)
Tn = 1 + (n-1)4.

By substituting the value for n, you can find the pattern.
Eg:
T5 = 1 +(5-1)4
T5 = 1 + (4) 4
T5 = 1 + 16
T5 = 17.

Similarly you can calculate for any n

Answer 6

this is an arithmetic progression.
first term (a)=1
c.d=5-1=4
nth shape=a+(n-1)d
=1+(n-1)4
=1+4n-4
=4n-3
put value of n find ans
all the best!

Answer 7

Un = a + (n-1)d
a = first term
a = 1

Un = 1 + (n-1)d
U3 = 9
9 = 1 + (3 - 1)d
8 = 2d
d = 4

Your formula is:
Un = 1 + (n-1)4
Un = 1 +4n - 4
Un = 4n - 3

Answer 8

This is an arithemetic progession. Formula is 4n-3 where n is position required

Answer 9

First term = 1 = 4*1 - 3
Second term = 5 = 4*2 - 3
Third term = 9 = 4*3 - 3
Fourth term = 13 = 4*4 - 3
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nth term = 4*n - 3