Question

Find the general term (n^th term) and 23^rd term of the sequence 3, 1, –1, –3, ........... . 

Answer 1

The given sequence is 1, –1, –3, ...........

Now,

1 – 3 = –1 – 1

= –3 – (–1)

= –2

Hence, the given sequence is an A.P. with first term a = 3 and common difference d = –2.

The general term (n^th term) of an A.P. is given by

t_n = a + (n – 1)d

= 3 + (n – 1)(–2)

= 3 – 2n + 2

= 5 – 2n

Hence, 23^rd term = t₂₃

= 5 – 2(23)

= 5 – 46

= –41