NCERT Class X Chapter 5: Arithmetic Progression Example 8

Question:

Find the 11th term from the last term (towards the first term) of the AP : 10, 7, 4, . . ., – 62.

Given:

An Arithmetic Progression (AP): 10, 7, 4, ..., -62

To Find:

The 11th term from the last term.

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.

Solution:

First, find the common difference (d): d = 7 - 10 = -3

Next, find the number of terms (n) in the AP. 

We have a = 10, d = -3, and a_n = -62. 

Using the formula a_n = a + (n-1)d:

-62 = 10 + (n-1)(-3) 

⇒ -72 = (n-1)(-3) 

⇒ n-1 = 24 

⇒ n = 25

The 11th term from the last term is the (25 - 11 + 1)th term from the beginning, which is the 15th term from beginning.

Now, find the 15th term using the formula a_n = a + (n-1)d:

⇒ a₁₅ = 10 + (15-1)(-3) 

⇒ a₁₅ = 10 + 14(-3) 

⇒ a₁₅ = 10 - 42 = -32

Result:

The 11th term from the last term in the given AP 10, 7, 4, . . ., – 62 is -32.

Next question solution:

NCERT Class X Chapter 5: Arithmetic Progression Example 9.

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