Arithmetic Progressions Quiz 11

Question 1

The $n^{th}$ term of the series 1.3 + 3.5 + 5.7 + &hellip;&hellip;&hellip;&hellip;&hellip;.. is

Accepted Answer

$4n^2 - 1$

Answer

1 &ndash; 4n

Answer

$n^2 + 4$

Answer

$4n^2 + 1$

Question 2

If n arithmetic means are inserted between a and b, then the common difference is &hellip;&hellip;&hellip;&hellip;

Accepted Answer

$\frac{b-a}{n+1}$

Answer

$\frac{a+b}{n+1}$

Answer

$\frac{n+1}{b+a}$

Answer

$\frac{n+1}{b-a}$

Question 3

Sum to n terms of 1.2.3 + 2.3.4 + 3.4.5 + &hellip;&hellip;&hellip;&hellip;&hellip;&hellip; is .

Accepted Answer

$\frac{n(n+1)(n+2)(n+3)}{4}$

Answer

$\frac{n(n+1)(n+2)(n+3)}{6}$

Answer

$\frac{n(n+1)(n+2)}{2}$

Answer

$\frac{n(n+1)(n+2)(n+3)}{8}$

Question 4

$\frac{1+2+3+.......+n}{1+3+5+.....+(2n-1)} = $

Accepted Answer

$\frac{(n+1)}{2n}$

Answer

$\frac{2}{n}$

Answer

$\frac{n}{2}$

Answer

$\frac{(n-1)}{2}$

Question 5

If the common difference of an A.P is 1 and 6th term is $\frac{(4 \, cos^2 \alpha+1)}{cos^2 \alpha}$ , then first term is

Accepted Answer

$tan^2 \alpha$

Answer

$cot^2 \alpha$

Answer

$cosec^2 \alpha$

Answer

$sec^2 \alpha$

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