Question 1

What is the 10th term of the arithmetic progression (A.P.) 2, 7, 12, ...?

Accepted Answer

To find the 10th term of the A.P., we use the formula $an = a + (n - 1)d$. Here, the first term $a = 2$, the common difference $d = 7 - 2 = 5$, and the number of terms $n = 10$. Substituting these values into the formula: $a{10} = 2 + (10 - 1) 	imes 5 = 2 + 9 	imes 5 = 2 + 45 = 47$. Therefore, the

Question 2

If the sum of $n$ terms of an A.P. is given by $Sn = 3n^2 + 5n$, then find its 2nd term.

Accepted Answer

The second term of an A.P. can be found using the relation $a2 = S2 - S1$. First, calculate $S1$ (which is equal to $a1$): $S1 = 3(1)^2 + 5(1) = 3 + 5 = 8$. Next, calculate $S2$: $S2 = 3(2)^2 + 5(2) = 3(4) + 10 = 12 + 10 = 22$. Now, $a2 = S2 - S1 = 22 - 8 = 14$. Therefore, the correct option is B.

Question 3

What is the 5th term of the geometric progression (G.P.) 3, 6, 12, ...?

Accepted Answer

The $n$th term of a G.P. is given by $an = ar^{n-1}$. Here, the first term $a = 3$, the common ratio $r = 6 / 3 = 2$, and $n = 5$. Substituting these values: $a5 = 3 	imes (2)^{5-1} = 3 	imes 2^4 = 3 	imes 16 = 48$. Therefore, the correct option is A.

Question 4

Which term of the G.P. 2, 4, 8, 16, ... is 512?

Accepted Answer

Using the formula for the $n$th term of a G.P., $an = ar^{n-1}$. Here, $a = 2$, $r = 2$, and $an = 512$. So, $512 = 2 	imes 2^{n-1}$, which means $256 = 2^{n-1}$. Since $256 = 2^8$, we have $2^{n-1} = 2^8$, giving $n - 1 = 8$, so $n = 9$. Therefore, the correct option is C.

Question 5

What is the arithmetic mean (A.M.) between 4 and 20?

Accepted Answer

The arithmetic mean of two numbers $a$ and $b$ is given by the formula $\frac{a + b}{2}$. Here, $a = 4$ and $b = 20$. Therefore, A.M. = $\frac{4 + 20}{2} = \frac{24}{2} = 12$. Thus, the correct option is B.

Sequences and Series