NCERT Class X Chapter 5: Arithmetic Progression Exercise 5.2 Question 4

Question:

Which term of the AP : 3, 8, 13, 18, . . . ,is 78?

Given:

Arithmetic Progression (AP): 3, 8, 13, 18, ...

Last term (a_n) = 78

To Find:

The term number (n) of the AP.

Formula:

The general term of an AP is given by:

a_n = a + (n - 1)d

where:

a_n = nth term

a = first term

n = number of terms

d = common difference

Solution:

Here, a = 3, d = 8 - 3 = 5, and a_n = 78.

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

78 = 3 + (n - 1)5

⇒ 78 - 3 = (n - 1)5

⇒ 75 = (n - 1)5

⇒ 75 5 = n - 1

⇒ 15 = n - 1

⇒ n = 15 + 1 = 16

Result:

Therefore, the 16th term of the AP is 78.

Next question solution:

NCERT Class X Chapter 5: Arithmetic Progression Exercise 5.2 Question 5(i)

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