Question

The first five terms of a sequence are

7. 10, 13, 16, 19.... (a) what is the nth term of the sequence? (b) workout the 1000th term of the sequence.

Answer 1

(a) 7 + 3( n - 1 )

(b) 1006

Explanation:

ARITHMETIC SEQUENCE.

The number of term of an Arithmetic progression has the formular :

nth term = a + ( n - 1 ) d

a = 7

d = 10 - 7 = 3

nth term = 7 + ( n - 1 ) 3

= 7 + 3n - 3

= 7 + 3( n - 1 )

Therefore,

the nth term of the sequence

= 7 + 3( n - 1 )

(b) For the 1000th term

= 7 + 3 ( 1000-1 )

= 7 + ( 999 )

7 + 999 = 1006

Therefore,

the 1000th term = 1006