Question

The question below has two statements, I and Impark your answer as
Find the sum or a Geometric series 1, 3, 9, 27, 81_____ for N terms.
I. N^th term is 729.
II. Next term after the N^th term is thrice of it.

• A. Question can be answered by using any one statement alone, but not by using other statement alone.
• B. Question can be answered by using either of the statements alone.
• C. Question can be answered by using both the statements together, but it cannot be answered by using either of the statements alone.
• D. Question cannot be answered even by using both the statements together.

Answer 1

The Correct Option is A

In question we know the \(N\)^th term
and after it the term is thrice of it so,
Sum of terms of G.P. = \(\frac{a(r^n - 1)}{r - 1}\)
Now, using the first statement, if we know the n^th term, then we can find the value of \(n\) and hence the sum of \(n\) terms.
Moving to the second statement which states that the next term after the \(N\)^th term is thrice of it, which only means that the common ratio of r=3, so we cannot find the sum using this statement.
So, this question can be answered by using only one statement alone.
The correct option is (A)