Question

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

Answer 1

Answer:

Hey Mate!!

Let nth term of an AP be represented by  $a_n$.

⇝ a₇ = a + (7 - 1)d = a + 6d

a₁₁ = a + (11 - 1)d = a + 10d

Now given,

7 × a₇ = 11 × a₁₁

⇝ 7(a + 6d) = 11(a + 10)d

⇝ 7a + 42d = 11a + 110d

⇝ 11a - 7a = -110d + 42d

⇝ 4a = -68d

⇝ 4a + 68d = 0

⇝ 4(a + 17d) = 0

⇝ a + 17d = 0

⇝ a + (18 - 1)d = 0

But, a + (18 - 1)d is the 18th term.

∴ a₁₈ = 0

Answer 2

☛ Question :-

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

☛ To Find :-

• 18th term

☛ Formula to be used :-

• an = a + (n - 1) d

☛ Solution :-

an = a + (n - 1) d

• a = first term
• d = common difference

↦ a7 = a + (7 - 1) d = a + bd

↦ a7 = a + 6d ______( 1 )

⇒ a11 = a + (11 - 1) d = a + 10 d

⇒ a11 = a + 10d ______( 2 )

➞ 7 . a7 = 11 . a11 (given)

➞ 7 . (a + 6d) = 11 . (a + 10d)

➞ 7a + 42f = 11a + 110d

➞ 42d - 110d = 11a - 7a

➞ -68d = 4a

➞ a = -17d _______( 3 )

➵ a18 = a + (18 - 1) d

➵ a18 = a + 17d

➵ a18 = -17d + 17d (from eq 2)

➵ a18 = 0

☛ The 18th term will be 0