Given the formula, Sn=a 1-r^n/1-r, what is the sum of the first nine terms of the geometric series: 324, -108, 36, -12...

Mathematics

1 answer:

vlada-n [284]3 years ago

3 0

Answer:

243.01.

Step-by-step explanation:

The first term (a) = 324.

The common ratio (r) = -108/324 = -1/3.

So sum of 9 terms is:

S(9) = 324 * (1 - (-1/3)^9) / ( 1 - (-1/3)

= 324 ( 1 - (-0.00005076)) / 4/3

= 324 * 1.00005076 / 1.33333

= 243.012.

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Find 4ab when (a+b)=15 and (a-b)=12

Volgvan

A + b = 15 ..... eq 1
a – b = 12 ...... eq 2

So a = 15 – b
Substitute in eq 2 :

15 – b – b = 12
15 – 2b = 12
–2b = 12 – 15
b = 1.5

So a = 15 – 3/2 = 13.5

4ab = 4 x 13.5 x 1.5 = 81

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3 years ago

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The sum of squares of two consecutive odd numbers is 514 find the numbers

amid [387]

Correct Question : The sum of squares of two consecutive positive odd numbers is 514. Find the numbers.

$\rule{130}1$

Solution :

Let the two consecutive positive odd numbers be x and (x + 2)

$\rule{130}1$

☯ $\underline{\boldsymbol{According\: to \:the\: Question\:now :}}$

$:\implies\sf x^2 + (x + 2)^{2} = 514 \\\\\\:\implies\sf x^2 + x^2 + 4x + 4 = 514\\\\\\:\implies\sf 2x^2 + 4x + 4 = 514 \\\\\\:\implies\sf 2x^2 + 4x = 514 - 4\\\\\\:\implies\sf 2x^2 + 4x = 510 \\\\\\:\implies\sf 2x^2 + 4x - 510 = 0\\\\\\:\implies\sf x^2 + 2x - 255 = 0 \:\:\:\:\:\Bigg\lgroup \bf{Dividing\:by\:2}\Bigg\rgroup\\\\\\:\implies\sf x^2 + 17x - 15x - 255 = 0\\\\\\:\implies\sf x(x + 17) - 15(x + 17) = 0\\\\\\:\implies\sf (x + 17) (x - 15)\\\\\\:\implies\sf x = - 17\:or\:x = 15\\\\\\:\implies\underline{\boxed {\sf x = 15}}\:\:\:\:\:\Bigg\lgroup \bf{Positive\:odd\: number}\Bigg\rgroup$