Answer:
S1: 2
S2:7
S3: 15
Step-by-step explanation:
Sn: 2 + 5 + 8 + . . . + ( 3n - 1) = n(1 + 3n)/2
S1: Put n = 1
[tex]= \frac{n (1 + 3n)}{2} \\= \frac{1 (1 + 3(1))}{2}\\= \frac{1 (1 + 3)}{2}\\= \frac{1(4)}{2}\\= \frac{4}{2}\\= 2[/tex]
S2: Put n = 2
[tex]= \frac{n (1 + 3n)}{2}\\= \frac{2 (1 + 3(2))}{2}\\= \frac{2 (1 + 6)}{2}\\= \frac{2 (7)}{2}\\= \frac{14}{2}\\= 7[/tex]
S3: Put n = 3
\frac{n (1 + 3n)}{2}\\= \frac{3 (1 + 3(3))}{2}\\= \frac{3 (1 + 9)}{2}\\= \frac{3 (10)}{2}\\= \frac{30}{2}\\= 15[/tex]
How these are true:
S1: 2
S2: 2+ 5 = 7 (Sum of first two terms
S3: 2+5+8 = 15 (Sum of first three terms)
