Question

9th term and 15th term of an arithmetic sequence are 65 and 107 respectively. a) what is the common difference. b) find 25h term of the sequence​

Answer 1

Answer:

d=7

a25=177

Step-by-step explanation:

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Answer 2

Answer :-

1. Common difference = 7
2. 25th term = 177

Given :-

• 9th term = a₉ = 65
• 15th term = a₁₅ = 107

To find :-

→ Common difference = d = ?

→ 25th term = a₂₅ = ?

Solution :-

We know that

➝ aₙ = a + (n - 1)d

a₉ = a + (9 - 1)d

➝ 65 = a + 8d.          -------- [Equation 1]

Similarly,

a₁₅ = a + (15 - 1)d

➝ 107 = a + 14d.        -------- [Equation 2]

[Equation 2] - [Equation 1]

               107 = a + 14d

          {-}    65 = a + 8d  

                   42 = 6d

→ 6d = 42

→ d = 42 ÷ 6

∴ d = 7

Substitute the value of d in equation 1 to find a.

a = 65 - 8d

➝ a = 65 - 8(7)

➝ a = 65 - 56

➝ a = 9

Now, for finding 25th term,

a₂₅ = a + (25 - 1)d

➝ a₂₅ = a + 24d

➝ a₂₅ = 9 + 24(7)

➝ a₂₅ = 9 + 168

➝ a₂₅ = 177