If $\alpha$ and $\beta$ are the roots of $ax^2 + bx + c = 0$:

Solve: $2x^2 + 7x + 6 = 0$

Sequence: An ordered list of numbers.
Arithmetic Progression (A.P.): A sequence where the difference between consecutive terms is constant.
Common Difference ($d$): $d = t_{n+1} - t_n$ (constant).
First Term: $a$ or $t_1$.
$n^{th}$ term of an A.P.: $$ t_n = a + (n-1)d $$
Sum of the first $n$ terms of an A.P. ($S_n$): $$ S_n = \frac{n}{2} [2a + (n-1)d] $$ or $$ S_n = \frac{n}{2} [t_1 + t_n] $$

Find the 10th term and sum of the first 10 terms of the A.P. $2, 5, 8, \dots$

Here $a=2, d=5-2=3$.
$t_{10} = a + (10-1)d = 2 + 9(3) = 2 + 27 = 29$
$S_{10} = \frac{10}{2} [2(2) + (10-1)3] = 5 [4 + 9(3)] = 5 [4 + 27] = 5 \times 31 = 155$

GST (Goods and Services Tax): A consumption tax levied on goods and services.
Components of GST:
- CGST (Central GST): Tax levied by the Central Government.
- SGST (State GST): Tax levied by the State Government.
- UTGST (Union Territory GST): For Union Territories.
- IGST (Integrated GST): For inter-state trade, collected by the Central Government.
GST Rates: Vary (0%, 5%, 12%, 18%, 28%). CGST rate = SGST rate.
Taxable Value: The value on which GST is calculated.
Input Tax Credit (ITC): Tax paid on purchases can be used to reduce tax payable on sales.
- GST Payable = Output Tax - Input Tax
Shares: Smallest unit of company's capital.
- Face Value (FV): Value printed on the share certificate.
- Market Value (MV): Price at which shares are traded.
- Dividend: Part of profit distributed to shareholders (calculated on FV).
- Premium: MV > FV; Par: MV = FV; Discount: MV < FV.
Sum Invested: Number of shares $\times$ MV.
Rate of Return (RoR): $\frac{\text{Dividend Income}}{\text{Sum Invested}} \times 100$.
Brokerage: Commission paid to a share broker (calculated on MV).
- Total cost of buying: MV + Brokerage + GST on Brokerage.
- Amount received on selling: MV - Brokerage - GST on Brokerage.