Question

If 5th term of an arithmetic sequence is 38 and the 9 th term is 66.what is the 25 th term?

Answer 1

Required Answer :

The 25th term of arithmetic progression = 178

Given :

• 5th term of arithmetic progression = 38

• 9th term of arithmetic progression = 66

To find :

• 25th term of arithmetic progression = ?

Solution :

⇒ tₙ = a + (n - 1)d

where,

• a denotes the first term
• n denotes the number of term
• d denotes the common difference

⇒ t₅ = a + (5 - 1)d = 38

⇒ t₅ = a + 4d = 38 -----(1)

⇒ t₉ = a + (9 - 1)d = 66

⇒ t₉ = a + 8d = 66 -----(2)

Solving (1) and (2) :

⠀⠀⠀⠀⠀⠀⠀⠀⠀a + 4d = 38

⠀⠀⠀⠀⠀⠀⠀⠀⠀a + 8d = 66

⠀⠀⠀⠀⠀⠀⠀⠀⠀-⠀-⠀⠀⠀-

⠀⠀⠀⠀⠀⠀⠀⠀___________

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀- 4d = - 28

⠀⠀⠀⠀⠀⠀⠀⠀___________

⇒ - 4d = - 28

⇒ d = 28/4

⇒ d = 7

Substitute the value of d in equation (1) :

⇒ a + 4d = 38

⇒ a + 4(7) = 38

⇒ a + 28 = 38

⇒ a = 38 - 28

⇒ a = 10

Therefore,

• The first term of arithmetic progression = 10
• The common difference = 7

Calculating the 25th term of arithmetic progression :

⇒ t₂₅ = a + (n - 1)d

⇒ t₂₅ = 10 + (25 - 1)7

⇒ t₂₅ = 10 + (24)7

⇒ t₂₅ = 10 + 168

⇒ t₂₅ = 178

Therefore, the 25th term of arithmetic progression = 178

Answer 2

Answer:

The 25th term is 178

Step-by-step explanation:

According to question:

a₅ = a + 4d = 38 ---(1)

⇒ a = 38 - 4d --(2)

a₉ = a + 8d = 66 --(3)

Put value of a in eq--(3)

38 - 4d + 8d = 66

4d = 66 - 38

4d = 28

d = 28/4

d = 7

Put value of d in eq.--(2)

a = 38 - 4(7)

a = 38 - 28

a = 10

Now, 25th term is:

a₂₅ = a + 24d

= 10 + 24(7)

= 10 + 168

= 178