NCERT Class X Chapter 5: Arithmetic Progression Exercise 5.3 Question3(x)

NCERT Class X Chapter 5: Arithmetic Progression Exercise 5.3 Question 3 (x)

Question

In an AP: given l = 28, S = 144, and there are total 9 terms. Find a.

Given

l (last term) = 28, S (sum of terms) = 144, n (number of terms) = 9

To Find

a (first term)

Formula

Sum of an arithmetic progression = Sn = n 2 (a + l) and 

Last term of arithmetic progression is given by l = a + (n - 1)d

Solution

Using the formula for the sum of an AP, we have:

144 = 9 2 (a + 28)

⇒ 144 × 2 = 9(a + 28)

⇒ 288 = 9(a + 28)

⇒ 288 9 = a + 28

⇒ 32 = a + 28

⇒ a = 32 - 28

⇒ a = 4

Result

The first term (a) is 4.

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