Question

Here are the first five terms of an arithmetic sequence.

26 19 12 5
(b) Find an expression, in terms of n, for the nth term of this sequence.

Answer 1

The nth term of an AP will be 27 -7n.

Explanation:

First five terms of the Arthemetic Sequence is given to us , which is 26 , 19 , 12 , 5

Hence here Common Difference can be found by subtracting two consecutive terms . Here which is 19 - 26 = (-7) .

Here first term is 26 .

And the nth term of an AP is given by ,

★ T_n = a + ( n - 1) d

Substituting respective values ,

⇒ T_n = a + ( n - 1 )d

⇒ T_n = 26 + (n - 1)(-7)

⇒ T_n = 26 -7n+1

⇒ T_n = 27 - 7n

Hence the nth term of an AP can be found using T_n = 27 - 7n.