Question

. How many terms of the series 3 +9+27+ .......... amount to 363 ?
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Answer 1

Step-by-step explanation:

given series.is in G.P

a = 3, r = 3 and Sₙ = 363

Sn = a(rⁿ - 1) / r - 1 for |r| > 0|

363 = 3(3ⁿ ⁻ 1) / (3 - 1)

363 = 3(3ⁿ - 1) / 2

=> 363 * 2/3 = 3ⁿ - 1

=> 242 = 3ⁿ - 1

=> 243 = 3ⁿ

=> 3⁵ = 3ⁿ

=> n = 5

there are 5 terms which give a sum of 363

Answer 2

Answer:

There are 5 number of term of the given series .

Step-by-step explanation:

Explanation:

Given,  series is 3 + 9 + 27 ..........up to 363 .

Here we can see that given series is in G.P .

Formula for G.P is ,

Sum of n term = $\frac{a(r^n-1)}{r- 1}$ , where r is the common ration and a is first term and n stand for no. of term .

Step 1:

From the question we have ,

3 + 9 + 27 ..........amount  to 363 .

a = 3  , r = $\frac{9}{3}$ = 3  and $S_n$ = 363 .

Now from the  G.P formula ,

⇒$S_n$ = $\frac{3 (3^n - 1)}{3-1}$

⇒363 =  $\frac{3^{n+1} -3}{2}$  ⇒ 726 =  $3 ^{n+ 1}$ - 3

⇒729 = $3^{n+ 1}$  

⇒$3^{6} = 3 ^{n+1}$ ⇒  6 = n+ 1     [where $3^{6} and \ 3 ^{n+1}$ have same base   ]

⇒ n = 5 .

Final answer:

Hence , there are total 5 terms   of the series 3 + 9 + 27 ...... amount to 363.

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