alleryIn a G.P. the 5th term is 81 and the 2nd term is 3. The common ratio is:
- $\tfrac{1}{3}$
- 3
- 9
- 27
Show answer and solution
Correct answer: B. 3
We have ar⁴ = 81 and.
Then ar = 3 ⟹ r³.
That is ar = 27 ⟹ r.
So ar = 3.
Karnataka PUC I Sequences and Series — practice questions — page 2
Explore 50 free Sequences and Series questions in Karnataka PUC I Mathematics. Open each question or exercise to read its content, reference answers and available explanation.
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In a G.P. the 5th term is 81 and the 2nd term is 3. The common ratio is:Read the answer and worked solution →The sum of the first 20 terms of an A.P. with first term 2 and common difference 3 is:Read the answer and worked solution →For $x > 0$, the minimum value of $x + \dfrac{4}{x}$ is:Read the answer and worked solution →If the sum of two positive numbers is 6 times their geometric mean, the numbers are in the ratio:Read the answer and worked solution →The value of $n$ for which $\dfrac{a^{n+1}+b^{n+1}}{a^{n}+b^{n}}$ is the geometric mean of $a$ and $b$ is:Read the answer and worked solution →Three numbers in G.P. have product 216 and sum 19. The numbers are:Read the answer and worked solution →If the A.M. and G.M. of the roots of a quadratic equation are 8 and 5 respectively, the equation is:Read the answer and worked solution →For two positive numbers, the arithmetic mean equals the geometric mean if and only if:Read the answer and worked solution →The sum $1^2 + 2^2 + \cdots + n^2$ equals:Read the answer and worked solution →The $n^\text{th}$ term of an Arithmetic Progression (AP) with first term $a$ and common difference $d$ isRead the answer and worked solution →The sum of the first $n$ terms of an AP with first term $a$ and last term $l$ isRead the answer and worked solution →The 10th term of an AP with first term $a = 5$ and common difference $d = 3$ isRead the answer and worked solution →The $n^\text{th}$ term of a Geometric Progression (GP) with first term $a$ and common ratio $r$ isRead the answer and worked solution →The sum of the first $n$ terms of a GP with first term $a$ and common ratio $r \neq 1$ isRead the answer and worked solution →The sum to INFINITY of the GP $1 + 1/2 + 1/4 + 1/8 + \ldots$ isRead the answer and worked solution →The Arithmetic Mean (AM) of two positive numbers $a$ and $b$ isRead the answer and worked solution →The Geometric Mean (GM) of $4$ and $9$ isRead the answer and worked solution →Sum of the first $n$ natural numbers, $1 + 2 + 3 + \ldots + n$, equalsRead the answer and worked solution →Sum of the SQUARES of the first $n$ natural numbers, $1^2 + 2^2 + 3^2 + \ldots + n^2$, equalsRead the answer and worked solution →Sum of the CUBES of the first $n$ natural numbers, $1^3 + 2^3 + \ldots + n^3$, equalsRead the answer and worked solution →
Worked practice questions
The sum of the first 20 terms of an A.P. with first term 2 and common difference 3 is:
- 305
- 590
- 620
- 610
Show answer and solution
Correct answer: D. 610
We have Sₙ = n/2[2a+(n−1)d].
That is Sₙ = 20/2[4 + 19·3].
That is Sₙ = 10[4+57].
So Sₙ = 610.
For $x > 0$, the minimum value of $x + \dfrac{4}{x}$ is:
- 8
- 1
- 4
- 2
Show answer and solution
Correct answer: C. 4
By AM–GM, x + 4/x ≥ 2√(x·4/x) = 2·2 = 4, attained at x = 2.
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