Question

Find the 54th term of the arithmetic sequence-7, -23, -39, ...

Answer 1

The 54th term in the given sequence is - 855.

Explanation:

Here, the terms of the sequence AP are : -7 , - 23 , - 39

Here, a2 - a1 = -23 - (-7) = -23 + 7 = -16

a3 - a2 = -39 - (-23) = - 39 + 23 = -16

So, here the common difference(d) of AP = -16

and first term (a) = -7 , n = 54

Now, in any AP :
`a_((n))  =  a + ( n -1) d`

So, for n = 54 :

`a_((54))  =  -7  + ( 54 -1) (-16)`

= -7 + 53(-16)

= -7 - 848 = - 855

⇒a(54) = - 855

Hence, the 54th term in the given sequence is - 855.