Chapter 12: Q 12.31. (page 1179)

Find the eleventh term of a sequence where the ninth term is 8 and the common difference is −3. Give the formula for the general term.

Short Answer

Expert verified

The eleventh term is 2 and the general term is $a_{n} = 35 - 3 n$ .

Step by step solution

Step 1. Given Informaation.

The ninth term is 8 and the common difference is −3.

Step 2. Find the first term by using the arithmetic formula.

Substitute 9 for n,-3 for d, and the ninth term are 8, in the formula $a_{n} = a_{1} + (n - 1) d$ .

role="math" localid="1645273827790" $\begin{array}{rcl} a_{9} & = & a_{1} + (9 - 1) (- 3) \\ 8 & = & a_{1} + (8) (- 3) \\ a_{1} & = & 8 + 24 \\ = & 32 \end{array}$

Step 3. Find the eleventh term.

Use the first term and common difference to find the eleventh term.

$\begin{array}{rcl} a_{11} & = & 32 + (11 - 1) (- 3) \\ = & 32 - 30 \\ = & 2 \end{array}$

Step 4. Find the general terms.

To find the general terms, substitute the first term 32 and the common difference -3 in the formula.

$\begin{array}{rcl} a_{n} & = & 32 + (n - 1) (- 3) \\ = & 32 - 3 n + 3 \\ = & 35 - 3 n \end{array}$

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Find the eleventh term of a sequence where the ninth term is 8 and the common difference is −3. Give the formula for the general term.

Short Answer

Step by step solution

Step 1. Given Informaation.

Step 2. Find the first term by using the arithmetic formula.

Step 3. Find the eleventh term.

Step 4. Find the general terms.

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