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1 . The second and third term of a geometric series are 9 and 3 respectivelt ,. The 6 th term of the series is-

A. 0
B. 1/3
C. 1
D. 1/9

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Answer: Option D

Explanation:

To find the 6th term of the geometric series, we can first find the common ratio (r) of the series. The common ratio can be found by dividing the third term by the second term:

r = 3rd term / 2nd term = 3 / 9 = 1/3

Now that we have the common ratio, we can use it to find the 6th term (T6) using the formula for the nth term of a geometric series:

Tn = a * r^(n-1)

Where: Tn = nth term a = first term r = common ratio

In this case, the first term (a) is not given, but we can find it using the second term and the common ratio:

a = 2nd term / r = 9 / (1/3) = 9 * 3 = 27

Now that we have the first term, we can find the 6th term:

T6 = 27 * (1/3)^(6-1) = 27 * (1/3)^5 = 27 * (1/243) = 1/9

So, the 6th term of the geometric series is 1/9.

সমন্বিত ৭ ব্যাংক ও ১টি আর্থিক | সিনিয়র_অফিসার | 27-11-2021

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