Study the following linear number pattern : 87; 78; 69; …
1 Determine the value of .
2 Which term has a value of 15 ?
3 Which term is the last term smaller than -60 ?
4 Which term is the first term greater than -94 ?
5 Which term is the first negative term?

Question

Study the following linear number pattern : 87; 78; 69; …
1 Determine the value of

.
2 Which term has a value of 15 ?
3 Which term is the last term smaller than -60 ?
4 Which term is the first term greater than -94 ?
5 Which term is the first negative term?

UpStudy AI · Accepted Answer

To solve the problem, we first need to identify the pattern in the given sequence: $$ 87, 78, 69, \ldots $$. 1. **Determine the common difference**: - The difference between consecutive terms is: - $$ 78 - 87 = -9 $$ - $$ 69 - 78 = -9 $$ - Thus, the common difference $$ d = -9 $$. 2. **General formula for the $$ n $$-th term**: - The formula for the $$ n $$-th term of an arithmetic sequence is given by: $$ T_n = a + (n - 1) \cdot d $$ - Here, $$ a = 87 $$ (the first term) and $$ d = -9 $$. Now, we can use this formula to answer the questions. ### 1. Determine the value of $$ T_{13} $$: $$ T_{13} = 87 + (13 - 1) \cdot (-9) $$ Calculating this: $$ T_{13} = 87 + 12 \cdot (-9) = 87 - 108 = -21 $$ ### 2. Which term has a value of 15? We need to find $$ n $$ such that: $$ T_n = 15 $$ Using the formula: $$ 15 = 87 + (n - 1) \cdot (-9) $$ Rearranging gives: $$ 15 - 87 = (n - 1) \cdot (-9) \implies -72 = (n - 1) \cdot (-9) $$ Dividing both sides by -9: $$ n - 1 = 8 \implies n = 9 $$ ### 3. Which term is the last term smaller than -60? We need to find the largest $$ n $$ such that: $$ T_n < -60 $$ Using the formula: $$ 87 + (n - 1) \cdot (-9) < -60 $$ Rearranging gives: $$ (n - 1) \cdot (-9) < -60 - 87 \implies (n - 1) \cdot (-9) < -147 $$ Dividing by -9 (and flipping the inequality): $$ n - 1 > 16.33 \implies n > 17.33 $$ Thus, the largest integer $$ n $$ is 17. ### 4. Which term is the first term greater than -94? We need to find the smallest $$ n $$ such that: $$ T_n > -94 $$ Using the formula: $$ 87 + (n - 1) \cdot (-9) > -94 $$ Rearranging gives: $$ (n - 1) \cdot (-9) > -94 - 87 \implies (n - 1) \cdot (-9) > -181 $$ Dividing by -9 (and flipping the inequality): $$ n - 1 < 20.11 \implies n < 21.11 $$ Thus, the smallest integer $$ n $$ is 21. ### 5. Which term is the first negative term? We need to find the smallest $$ n $$ such that: $$ T_n < 0 $$ Using the formula: $$ 87 + (n - 1) \cdot (-9) < 0 $$ Rearranging gives: $$ (n - 1) \cdot (-9) < -87 $$ Dividing by -9 (and flipping the inequality): $$ n - 1 > 9.67 \implies n > 10.67 $$ Thus, the smallest integer $$ n $$ is 11. ### Summary of Results: 1. $$ T_{13} = -21 $$ 2. The term with a value of 15 is $$ T_9 $$. 3. The last term smaller than -60 is $$ T_{17} $$. 4. The first term greater than -94 is $$ T_{21} $$. 5. The first negative term is $$ T_{11} $$. 1. $$ T_{13} = -21 $$ 2. The term with a value of 15 is $$ T_9 $$. 3. The last term smaller than -60 is $$ T_{17} $$. 4. The first term greater than -94 is $$ T_{21} $$. 5. The first negative term is $$ T_{11} $$.

Study the following linear number pattern : 87; 78; 69; …
1 Determine the value of .
2 Which term has a value of 15 ?
3 Which term is the last term smaller than -60 ?
4 Which term is the first term greater than -94 ?
5 Which term is the first negative term?

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Study the following linear number pattern : 87; 78; 69; … 1 Determine the value of . 2 Which term has a value of 15 ? 3 Which term is the last term smaller than -60 ? 4 Which term is the first term greater than -94 ? 5 Which term is the first negative term?

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Latest Algebra Questions

Study the following linear number pattern : 87; 78; 69; …
1 Determine the value of .
2 Which term has a value of 15 ?
3 Which term is the last term smaller than -60 ?
4 Which term is the first term greater than -94 ?
5 Which term is the first negative term?