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Sum of the series 1 + 3 + 9 + 27 +….is 364. The number of terms is
  • a)
    5
  • b)
    6
  • c)
    11
  • d)
    none of these
Correct answer is option 'B'. Can you explain this answer?
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Sum of the series 1 + 3 + 9 + 27 +….is 364. The number of terms ...
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Sum of the series 1 + 3 + 9 + 27 +….is 364. The number of terms ...
Given series: 1, 3, 9, 27, ...

To find the number of terms, we can use the formula for the sum of a geometric series:

S = a(1 - r^n) / (1 - r)

where S is the sum of the series, a is the first term, r is the common ratio, and n is the number of terms.

We are given that S = 364, a = 1, and r = 3.

Substituting these values into the formula, we get:

364 = 1(1 - 3^n) / (1 - 3)

Simplifying this equation, we get:

-1092 = 1 - 3^n

Adding 1091 to both sides, we get:

1091 = 3^n

Taking the logarithm of both sides, we get:

n log 3 = log 1091

Dividing both sides by log 3, we get:

n = log 1091 / log 3 ≈ 5.6

Since the number of terms must be a whole number, we round up to the nearest integer to get:

n = 6

Therefore, the number of terms in the series is 6, which is option B.
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Sum of the series 1 + 3 + 9 + 27 +….is 364. The number of terms isa)5b)6c)11d)none of theseCorrect answer is option 'B'. Can you explain this answer?
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