Question

Find the 30th term from the end of the AP 3,8,13.........253​

Answer 1

Answer:

108

Step-by-step explanation:

Given :

3, 8, 13, , .......... 253 are in AP

First term of the AP ( a ) = 3

Common difference of the AP  ( d ) = a₂ - a₁ = 8 - 3 = 5

Let  aₙ  = 253 and ' n ' be the number of terms

Using nth term of AP formula

aₙ = a + ( n - 1 )d

⇒ 253 = 3 + ( n - 1 )5

⇒ 253 - 3 = ( n - 1 )5

⇒ 250/5 = n - 1

⇒ 50 = n - 1

⇒ 50 + 1 = n

⇒ 51 = n

⇒ n = 51

Hence the AP has 51 terms and 30th term from the end would be 22th term and lets find it using formula.

Using nth term of AP formula

⇒ aₙ = a + ( n - 1 )d

⇒ a₂₂ = 3 + ( 22 - 1 )5

⇒ a₂₂ = 3 + 21( 5 )

⇒ a₂₂ = 3 + 105

⇒ a₂₂ = 108

Therefore the 30th term from the end of AP is 108.