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MCQ

Fill in the Blanks

If 7 times the 7^{th} term of an AP is equal to 11 times its 11^{th} term, then its 18^{th} term will be ______.

#### Options

7

11

18

0

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#### Solution

If 7 times the 7^{th} term of an AP is equal to 11 times its 11^{th} term, then its 18^{th} term will be **0**.

**Explanation:**

`7a_7 = 11a_11`

⇒ `7[a + (7 - 1)d] = 11[a + (11 - 1)d]` ....`[because a_n = a + (n - 1)d]`

⇒ `7(a + 6d) = 11(a + 10d)`

⇒ `7a + 42d = 11a + 110d`

⇒ `4a + 68d` = 0

⇒ `2(2a + 34d)` = 0

⇒ `2a + 34d` = 0 ....[∵ 2≠ 0]

⇒ `a + 17d` = 0 ......(i)

∴ 18^{th} term of an AP, `a_18 = a + (18 - 1)d`

= `a + 17d` = 0 .....[From equation (i)]

Concept: Arithmetic Progression

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