NCERT Class X Chapter 5: Arithmetic Progression Exercise 5.2 Question 17

Question:

Find the 20th term from the last term of the AP : 3, 8, 13, . . ., 253.

Given:

An Arithmetic Progression (AP): 3, 8, 13, ..., 253

To Find:

The 20th term from the last term of the AP.

Formula:

The nth term of an AP is given by a_n = a + (n-1)d, where 

a is the first term and 

d is the common difference.

 

Also, nth term from the last term (l) = (l - n - 1 )th term from the first term

Solution:

The common difference (d): d = 8 - 3 = 5

The nth term is given by a_n = a + (n-1)d.
We have,
253 = 3 + (n-1)5
⇒ 250 = (n-1)5
⇒ n-1 = 50
⇒ n = 51

We want the 20th term from the last term, which is equal to the (51 - 20 + 1)th term from the first term i.e 32nd term.

Now we find the 32nd term: 

⇒ a₃₂ = 3 + (32-1)5 

⇒ a₃₂ = 3 + 31(5) 

⇒ a₃₂ = 3 + 155 

⇒ a₃₂ = 158

Result:

The 20th term from the last term is 158.

Next question solution:

NCERT Class X Chapter 5: Arithmetic Progression Exercise 5.2 Question 18

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