Question

If the 7th term and 3 th term 34 and 64 find the 18 th term

Answer 1

Appropriate Question :

If the 7th term and 13 th term of A.P. are 34 and 64 respectively. Find the 18 th term.

Required Answer :

The 18th term of A.P. = 89

Given :

• The 7th term of A.P. = 34
• The 13th term of A.P. = 64

To find :

• The 18th term of A.P.

Solution :

Formula to be used :

• tₙ = a + (n - 1)d

⇒ t₇ = a + (7 - 1)d = 34

⇒ t₇ = a + 6d = 34 -------(1)

⇒ t₁₃ = a + (13 - 1)d = 64

⇒ t₁₃ = a + 12d = 64 -----(2)

Solving (1) and (2) :

⠀⠀⠀⠀⠀⠀⠀⠀⠀a + 6d = 34

⠀⠀⠀⠀⠀⠀⠀⠀⠀a + 12d = 64

⠀⠀⠀⠀⠀⠀⠀⠀⠀-⠀-⠀⠀⠀⠀-

⠀⠀⠀⠀⠀⠀⠀⠀____________

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀- 6d = - 30

⠀⠀⠀⠀⠀⠀⠀⠀____________

⇒ - 6d = - 30

⇒ 6d = 30

⇒ d = 5

Substituting the value of d in equation 1 :

⇒ a + 6d = 34

⇒ a + 6(5) = 34

⇒ a + 30 = 34

⇒ a = 34 - 30

⇒ a = 4

Therefore,

• The common difference (d) = 5
• The first term of A.P. (a) = 4

Calculating the 18th term of A.P. :

⇒ tₙ = a + (n - 1)d

⇒ t₁₈ = 4 + (18 - 1)5

⇒ t₁₈ = 4 + (17)5

⇒ t₁₈ = 4 + 85

⇒ t₁₈ = 89

Therefore, the 18th term of A.P. = 89

Answer 2

Answer:

$\underline{\purple{\ddot{\Maths dude}}}$

◇◇Perfect question :-

• If the 7th term and 13th term of an Ap are 34 and 64 respectively, find 18th terms of an Ap

◇◇Given:-

• 7th terms of an AP is 34
• 13th terms of an AP is 64 .

◇◇To prove :-

• 18th term of an AP .

♧♧Explanation :-

a+6d=34 (i)

( - )a +12d=64

-6d=-30

d=-30/-6

d=+5.

♧♧Let , substitute the value of d =+5 on 1st equation ,

• a+6d =34
• a+6 (5)=34
• a +30=34
• a =34-30
• a = +4.

♤Here we should find 18th terms of an AP .

▪18th term of an AP

t18= a+17d

t18= 4+17 (5)

t18= 89.

♧♧Therefore, 18th term of an AP is 89.

♧♧Hope it helps u mate .

♧♧Thank you.