NCERT Class X Chapter 5: Arithmetic Progression Example 12

Question:

If the sum of the first 14 terms of an AP is 1050 and its first term is 10, find the 20th term.

Given:

Sum of first 14 terms (S₁₄) = 1050
First term (a) = 10

To Find:

20th term (a₂₀)

Formula:

S_n = n 2 [2a + (n - 1)d]
a_n = a + (n - 1)d

Solution:

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

1050 = 14 2 [2(10) + (14 - 1)d] ⇒ 1050 = 7[20 + 13d] ⇒ 150 = 20 + 13d ⇒ 13d = 130 ⇒ d = 10

Now, we find the 20th term using the formula for the nth term of an AP:

a₂₀ = a + (20 - 1)d = 10 + 19(10) = 10 + 190 = 200

Result:

The 20th term of the AP is 200.

Next question solution:

NCERT Class X Chapter 5: Arithmetic Progression Example 13

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