Question

Consider the sequence of numbers 2, 5, 8, 11, 14, . . ., in which each number is three more than its predecessor. (a) Find the next three numbers in the sequence. (b) Find the 100th number in the sequence. (c) Using the variable n to represent the position of a number in the sequence, write an expression that allows you to calculate the nth number. The 200th number in the sequence is 599. Verify that your expression works by evaluating it with n equal to 200.

Answer 1

(a) 17, 20, and 23.

(b) 299

(c)
`t_(200) =599` (Proved)

Explanation:

If we consider the sequence of numbers 2, 5, 8, 11, 14, ....... then it gives an A.P series with first trem(
`t_(1)`) = 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
`t_(100) = t_(1) + (100-1)d`

⇒
`t_(100) = 2+ 3 * 99=299` (Answer)

(c) So, the nth term of the A.P. will be given by

`t_(n)= t_(1)  + (n-1)d = 2+ (n-1)3` ..... (1)

Now, from equation (1) we get the 200th term as

`t_(200) = 2+ (200-1)3`

⇒
`t_(200) = 2 + 199 * 3 =599` (Proved)