Question

Given that 4, 12, x, y, 324, 972..... is a geometric sequence, find the sum of x and y.
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Answer 1

$\large{\underline{\sf{\red{Given-}}}}$

• 4, 12, x, y, 324, 972 is a geometric sequence.

$\large{\underline{\sf{\pink{To \: Find-}}}}$

• Sum of x & y.

$\large{\underline{\sf{\orange{Solution-}}}}$

Case 1 :

$\bf\longrightarrow{ \frac{12}{4} = \frac{x}{12} }$

$\bf\longrightarrow{ \frac{(12 \times 12)}{4} = x}$

$\bf\longrightarrow\dfrac{\cancel{(12 \times 12)}}{\cancel{4}} = x$

$\bf\longrightarrow{3 \times 12 = x}$

$\bf \star\underbrace{x = 36} \star$

Case 2 :

$\bf\longrightarrow{ \frac{y}{x} = \frac{12}{4} }$

$\bf\longrightarrow{ \frac{y}{x} = \dfrac{\cancel{12}}{\cancel{4}}}$

$\bf\longrightarrow{y = 3 \times 36}$

$\bf \star\underbrace{y = 108} \star$

Now,

Substituting Values,

$\bf\longrightarrow{x + y}$

$\bf\longrightarrow{36 + 108}$

$\bf \star\underbrace{x + y = 144} \star$

Hence,

• Sum of x & y is 144.

Answer 2

Answer:

Step-by-step explanation:

Geometric sequence formula isAn= A1*r^(n-1)3

A1=4,n=1

A2=12,n=2

Formula from A1 to A2 becomes 12=4*r^(1)

Which becomes 12=4*r

Solve for r to get r=12/4=3

A3=4*3^2=36

A4=4*3^3=108

A5=4*3^4=324

A6=4*3^4=972

Your sequence is 4,12,36,108,324,972

x=36

y=108

x+y=144.