Question

derive the formula tn =a+(n-1)d and Sn=n/2(2a+(n-2)d) also explain the difference in these two formulas and when they are used​

Answer 1

Answer:

Hello

Step-by-step explanation:

aa is the first term in the arithmetic sequence and dd is the common difference. The formula you describe is the sum of the first nn of the arithmetic sequence. For example, in the arithmetic sequence 2, 5, 8, 11, 14, 17, 20, 23, …, the first term is 2, which is aa. The common difference, dd, is 3. The sum of the first 5 terms is S5S5, where 5 is nn. So S5=5[2∗2+(5−1)∗3]2=40S5=5[2∗2+(5−1)∗3]2=40. This is indeed correct, as we see from the sequence that 2+5+8+11+14=402+5+8+11+14=40.