How many terms are there in the AP 1, 1 , …., –16 ?

To Find: we need to find number of terms in the given AP.

Given: The series is 1, 1, …., –16 .

a₁=1= , a₂= 1=, d=()–()= and a_n= –16 =

(Where a=a₁ is first term, a₂ is second term, a_n is nth term and d is common difference of given AP)

Formula Used: a_n = a + (n - 1)d

a_n= = a₁ + (n–1)()

– = (n–1)() [subtract on both sides]

= (n–1)() [Multiply both side by ] or [Divide both side by ]

27 = (n–1) [add 1 on both sides]

n =28

So there are 28 terms in this AP.