In an A.P., if a 18 - a 14 = 32 then the common difference is 1. 8 2. -8 3. -4 4. 4

Given, a 18 - a 14 = 32. We know that a n = a + (n - 1)d ∴ a 18 = a + (18 - 1) × d = a + 17d. a 14 = a + (14 - 1) × d = a + 13d. ∴ a 18 - a 14 = a + 17d - (a + 13d) = a - a + 17d - 13d = 4d. ⇒ 4d = 32 ⇒ d = 8. Hence, Option 1 is the correct option.

Mathematics

In an A.P., if a₁₈ - a₁₄ = 32 then the common difference is
8
-8
-4
4

AP GP

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Answer

Given, a₁₈ - a₁₄ = 32.

We know that

a_n = a + (n - 1)d
∴ a₁₈ = a + (18 - 1) × d = a + 17d.
a₁₄ = a + (14 - 1) × d = a + 13d.

∴ a₁₈ - a₁₄ = a + 17d - (a + 13d) = a - a + 17d - 13d = 4d.

⇒ 4d = 32
⇒ d = 8.

Hence, Option 1 is the correct option.

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Mathematics

In an A.P., if a₁₈ - a₁₄ = 32 then the common difference is
8
-8
-4
4

AP GP

Answer

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