Question

Check whether – 25 is a term in the progression 5, 3, 1, ………….or not ?

Answer 1

The given 5, 3, 1,…………..is an arithmetic progression here 

a = 5, d = a₂ – a₂ = 3 – 5 = -2 

Let -25 is some of ‘n’ th term 

i.e. a_n – 25 

So a_n = a + (n-1)d 

-25 = 5 + (n – 1)(- 2)

– 25 – 5 = (n – 1) (-2)

\(\frac{-30}{-2}\) = n – 1 

⇒  n – 1 = 15 and n = 15+ 1 = 16

So – 25 exist at 16th term in above series.