Question

Please answer the below question...

Answer 1

Answer:

The answer will be 5n+1.

where, n is the term to which we extend the pattern.

Step-by-step explanation:

In first combination, no. of matchstick = 6

In second, its = 11

and in third, no. of matchsticks = 16

Let's consider the no. of matchstick used in first pattern be a and no. of increased matchstick in consecutive (next one) pattern be d.

Thus, d = no. of matchsticks in second pattern - no. of matchsticks in first pattern

d = 11 - 6

= 5.

For all this given patterns, an appropriate rule will be;

an = a + d(n-1);

where, an = no. of matchsticks used in the nth term pattern.

a = 6 or no. of matchsticks used in 1st term.

d = 5 or by how much does the consecutive pattern differs in no. of matchsticks

n = term to which we want to extend our patterns

an = 6 + 5(n-1)

= 6 + 5n - 5

= 5n + 1

5n + 1 will be a suitable rule for the given patterns.

For example: If we want to find the no. of matchsticks used in 16th term pattern then the solution will be;

a16 = 5(16) + 1

a16 = 80 + 1

= 81.

So the no. of matchsticks used in 16th term pattern is 81.

That's all.