Check whether – 25 is a term in the progression 5, 3, 1, ………�

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

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

Answer»

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.