Question

The 12th term of an arithmetic sequence is
25 and the common difference is 3. What
is the 17th term?​

Answer 1

Answer:

The 17th term is equal to the first term plus the difference of 17 and 1. So d = 2. The first term is 7, the common difference is 2 and the 17th term = a+16d = 7+32 = 39.

Answer 2

$\Large \underline{ \underline{ \bf \purple{Given :}}}$

• 12th termof A.P = 25

• Common difference = 3

$\Large \underline{ \underline{ \bf \purple{To \: Find :}}}$

• 17th term of the given A.P

$\Large \underline{ \underline{ \bf \purple{Solution :}}}$

$\begin{gathered}\longrightarrow \sf A_{12} = a + 11d \\ \\\longrightarrow \sf 25 = a + 11 \times 3 \\ \\\longrightarrow \sf 25 = a + 33 \\ \\\longrightarrow \sf a = 25 - 33 \\ \\\longrightarrow \underline{\boxed{ \sf a = - 8}}\end{gathered}$

Now , 17th term of the A.P

$\begin{gathered}\longrightarrow \sf A_{17} = a + 16d \\ \\\longrightarrow \sf A_{17} = - 8 + 16 \times 3 \\ \\\longrightarrow \sf A_{17} = - 8 + 48 \\ \\ \longrightarrow \underline{ \boxed{ \sf \orange{A_{17} =40}}}\end{gathered}$