There are 50 seashells on the beach. After one week there are 120 seashells on the beach. If this same pattern continues how many seashells will there be on the 4th week?

Step-by-step explanation:

Given:

Initial amount, a = 50 seashells

Amount at 1st week, a1 = 120 seashells

Using arithmetic sequence,

an = ao + (n - 1) d

Where,

an = amount of seashells at n weeks

ao = initial amount of seashells

n = number of weeks

d = common difference (constant)

Finding d,

d = an+1 - an

= a1 - ao

d = 120 - 50

= 70

At week 4,

a4 = ao + 3d

= 120 + (3 * 70)

= 50 + 210

= 260 seashells

260 seashells

Step-by-step explanation:

If there are 50 seashells on the beach and after one week there are 120 seashells on the beach and this same pattern continues, then the number of sea shells form weekly will form an arithmetic progression.

The sequence formed will be;

50,120 ...

To find the number of seashells that we will have in the 4th week is equivalent to finding the 4th term of the sequence.

The formula for calculating the nth term of a sequence is as given below;

Tn = a + (n-1) d where;

a is the first term

n is the number of terms

d is the common difference.

According to the sequence;

a = 50,

d = 120-50 = 70

n = 4 (since we are looking for the 4th term)

Substituting this values in the given formula we have;

T4 = 50 + (4-1) 70

T4 = 50+3 (70)

T4 = 50+210

T4 = 260

This means that there will be 260seashells on the 4th week if the same pattern continues.