# If 7 times the 7th term of an AP is equal to 11 times its 11th term, then its 18th term will be ______. - Mathematics

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

• 7

• 11

• 18

• 0

#### Solution

If 7 times the 7th term of an AP is equal to 11 times its 11th term, then its 18th 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)

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

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

Concept: Arithmetic Progression
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#### APPEARS IN

NCERT Mathematics Exemplar Class 10
Chapter 5 Arithematic Progressions
Exercise 5.1 | Q 12 | Page 46
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