nicekikah

2020-10-18

Consider the sequence $67,63,59,55......$ 1. show that the sequence is arithmetic. 2. find a formula for the general term Un. 3. Find the 60th term of the sequence. 4. Is -143 a member of the sequence? 5. Is 85 a member of the sequence?

escumantsu

Skilled2020-10-19Added 98 answers

Step 1 Observe the following series: $67,63,59,55...$ Step 2 The terms of the series can be denoted as follows: ${a}_{1}=67,$

${a}_{2}=63,$

${a}_{3}=59,$

${a}_{4}=55,$ Step 3 Check the series' type now.: ${a}_{1}-{a}_{2}=67-63=4,$

${a}_{2}-{a}_{3}=63-59=4,$

${a}_{3}-{a}_{4}=59-55=4,$ Since ${a}_{1}-{a}_{2}={a}_{2}-{a}_{3}={a}_{3}-{a}_{4}=4,$ Hence series is arithmetic Step 4 The formula for the nth term is determined as follows: ${a}_{1}=67,$

${a}_{2}=63,$

${a}_{2}={a}_{1}-4\cdot (2-1),$

${a}_{3}=59,$

${a}_{3}={a}_{1}-4(3-1),$ Now decide. thr ${6}^{th}$ term sa follows: ${a}^{60}={a}_{1}-4(60-1)$

${a}^{60}=67-4\cdot 59$

${d}^{60}=169$

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