Question

23 + (-8) - 7 9 - 13 + 12​

Answer 1

Answer:

Step-by-step explanation:

Here is the problem 7,9,13,21,37,?

Every person has various ways to determine the solution, I have also a solution i.e.

Let us assume that sum of all the terms(which are know as well as unknown) is Sn.

Sn=7+9+13+21+37+………+A(n-1)+An.____say eq.1

Now if we take this sum in such a way …….

Sn=_7+9+13+21+37+……..+A(n-2)+A(n-1)+An.

Say it eq.2

Now subtract both the equations.

eq.1-eq.2

Sn=7+9+13+21+37+…..A(n-1)+An.

Sn=_+7+9+13+21+……A(n-2)+A(n-1)+An.

After subtracting we get

0=7+[2+4+8+16+32+………A(n-1)]-An

Replacing An in RHS.

An=7+[2+4+8+16+32+…….A(n-1)]______eq(*)

Here terms inside big bracket is known as geometrical progression( GP)

Geometrical progression is a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.

Sum of GP=A+Ar^1+Ar^2+…Ar^n.

So the sum of GP, first term is A and common ratio is r having (n-1) terms….. is {A*[r^(n-1)-1]}/{[r-1]}

Calculation of r(common ratio) is [second term/first term] or [third term/second term] or [An/A(n-1)].

So that from eq(*)

An=7+{2*[2^(n-1)-1]}/{[2–1]}

An=7+(2^n-2)/1

An=7+2^n-2

An=5+2^n…(this is the general term)

Put values of n=1,2,3,4,5,6……..n

A1=5+2^1=7

A2=5+2^2=9

A3=5+2^3=13

.

.

A6=5+2^6=69(this is the answer)

So sequence will be …7,9,13,21,37, 69,133….

Thanks …!!!

Answer 2

Answer:

here is your answer in the attachment

hope it helps mark as brainliest please