Question

if 1+2+4+8+............n term=255,then option is 8 and b option is 9 and c option is 12 and d option is 15 . which is correct​

Answer 1

Answer:

i know this answer but not sure sorry :(

Answer 2

Answer:

Step-by-step explanation:

ANSWER:-

When we try to attempt this question, we attempt the progression called Geometric Progressions. In default there are 3 types:-

• Arithmetic Progression
• Geometric progression
• Harmonic progression

So, we will be using GP or Geometric Progression formulas.

$\boxed{\sf{S_n = \dfrac{a(r^n-1)}{r-1}}}$

Where $\sf{S_n}$ is the sum of all the terms

Where a is first term

r is common ratio, where it is 2, as $\dfrac{2}{1}$ first term and second term gives 2.

And n is the number of terms, which we actually need to find.

$\sf{255 = \dfrac{1(2^n-1)}{2-1}}$

$\sf{255 = \dfrac{1(2^n-1)}{1}}$

$\sf{255 = 2^n-1}$

$\sf{255+1 = 2^n}$

$\sf{256 = 2^n}$

Converting it to base of two,

$\sf{2^8 = 2^n}$

$\boxed{\sf{n = 8}}$

So, 8 is the correct option. Hence, a part is the correct answer.

Similar Formulas:-

In AP, we have sum of terms as:-

$\boxed{\sf{S_n = \dfrac{n}{2} \times( 2a+(n-1)\times d)}}$

Where S_n is the sum of terms

a is the first term

d is the common difference

In HP or Harmonic Progressions, we have the reciprocal of AP one.

$\boxed{\sf{a_n =\dfrac{1}{a+ (n-1)d}}}$

The symbols have their usual meanings, just the reciprocal needs to be done. But, there is no concise or proper formula for the sum of HP. The formula written above is used to determine the 'n'th term of the progression.

Also Note:-

For infinite geometric progression, if we have -1<r<1 or |1|<1, this will be considered as Infinite GP. Hence:-

$\boxed{\sf{S_\infty = \dfrac{a}{1-r}, if \ |r|<1}}$

The sum of Infinite progression is represented as $\sf{S_\infty}$ in the formula, else if all have their usual meanings.

Relation in AP, GP and HP:-

$\boxed{\sf{Arithmetic \ Progression \times Harmonic \ Progression = (Geometric \ Progression)^2}}$

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