Question

In a GEOMETRIC sequence, t2+t3=60 , and t5+t6=3840
Write the first three terms.

Answer 1

Answer: The first three terms of G.P. will be 3,12,48

Step-by-step explanation:

In mathematics, a geometric progression (GP) is a type of sequence where each successive term is formed by multiplying each preceding term by a fixed number called a common ratio. This procedure is also known as a geometric sequence of numbers that follow a pattern. Learn arithmetic progression here too. The common ratio multiplied here by each term to get the next term is a non-zero number. An example of a geometric sequence is 2, 4, 8, 16, 32, 64, ..., where the common ratio is 2.

A geometric sequence or geometric sequence is a sequence in which each term is interchanged with another in a common ratio. The next term of the sequence is formed when we multiply a constant (which is non-zero) by the previous term. It is represented by:

$a, ar, ar^2, ar^3, ar^4$ and so on.

Where a is the first term and r is the common ratio.

Since the general term of G.P. is $ar^{n-1}$ hence t2,t3,t5,t6 will be$ar^1, ar^2, ar^4,ar^5$ respectively.

Now according to the given equations:

t2+t3=60 i.e.

$ar^1+ar^2=60$

ar(r+1)=60.......(1)

Alsot5+t6=3840

$ar^4+ar^5=3840\\ar^4(r+1)=3840..(2)$

Divide (1) and (2) we get,

$r^3=64$

Hence r=4

Now put the value of r in (1) to get the value of a which is

$a*4(4+1)=60$

20a=60

a=3

Now the first three terms of G.P. will be $a,ar,ar^2$ which will be

$3,3*4,3*4^2$ or

3,12,48

Hence the first three terms of G.P. will be 3,12,48

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