Question 2
In an arithmetic progression, the 8th term is twice the 3rd term and the 20th term is 110.
a) Find the common difference.

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Let the first term be \( a \), and the common difference be \( d \).

The formula for the \( n \)-th term is:

\[ a_n = a + (n - 1)d \]

The 8th term is twice the 3rd term:

\[ a + 7d = 2(a + 2d) \]

Open the brackets:

\[ a + 7d = 2a + 4d \]

Move terms:

\[ 3d = a \]

So \( a = 3d \).

The 20th term is 110:

\[ a + 19d = 110 \]

Substitute \( a = 3d \):

\[ 3d + 19d = 110 \]

\[ 22d = 110 \]

\[ d = 5 \]

Answer: the common difference is \( 5 \).

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