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## In round 1 of a phone tres a person calls four people n round two ea person calls 4 more people and so on how nany calls will be nade by roynd 5

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# 1 Answer

Hi Mikk,

I am not sure if I understood the question correctly.

**First interpretation of question:**

in Round 1, the person called 4 people and in the next rounds, the 4 people will call another 4 people each, and so on.

If that is the case, number of calls in:

round 5 is 4

^{5}round 4 is 4

^{4}round 3 is 4

^{3}round 2 is 4

^{2 and}round 1 is 4.

Note that this is a geometric progression. So when we find the sum, we are finding the geometric series. The formula to find geometric series up to n terms is:

(a(1-r

^{n}))/(1-r),where a is the first term and r is the common ratio of the sequence.

So when you add them up:

4+4

^{2}+4^{3}+4^{4}+4^{5}.first term, a = 4,

common ratio = 4

number of terms = 5

Applying the formula:

4+4

^{2}+4^{3}+4^{4}+4^{5}= (4(1-4

^{5}))/(1-4)=1364

The

**second interpretation**of the question could be one person called 4 people in round 1 and in round 2 he called 4 more people, which means he called 8 people in round 2, and in round, he called 4 more people than the previous round.If this is the case, number of calls in

round 1: 4

round 2: 8 i.e. 2*4

round 3: 3*4

round 4: 4*4

round 5: 5*4 = 20

In this case, this is an arithmetic progression. So if we add them up, it will be an arithmetic series. To add them up to n terms, the formula is

(n/2)(a+l) or (n/2)(2a+(n-1)d)

where a is the first term, l is the last term of the series and d is the common difference.

For this question:

total number of calls by round 5

= (5/2)(4+20)

= 60

the other formula..

total number of calls by round 5

=(5/2)(2*4 + (5-1)4)

=60

Let me know if i interpreted the question correctly.