Answer:
(a) 17, 20, and 23.
(b) 299
(c) [tex]t_{200} =599[/tex] (Proved)
Step-by-step explanation:
If we consider the sequence of numbers 2, 5, 8, 11, 14, ....... then it gives an A.P series with first trem([tex]t_{1}[/tex]) = 2 and the common difference(d) = 3.
(a) Therefore, the next three terms of the sequence will be 17, 20, and 23. (Answer)
(b) The 100th term of the sequence will be [tex]t_{100} = t_{1} + (100-1)d[/tex]
⇒ [tex]t_{100} = 2+ 3 \times 99=299[/tex] (Answer)
(c) So, the nth term of the A.P. will be given by
[tex]t_{n}= t_{1} + (n-1)d = 2+ (n-1)3[/tex] ..... (1)
Now, from equation (1) we get the 200th term as
[tex]t_{200} = 2+ (200-1)3[/tex]
⇒ [tex]t_{200} = 2 + 199 \times 3 =599[/tex] (Proved)
