Let \dfrac{a}{b}" alt="\sf a+b,a-b,ab,\dfrac{a}{b}" align="absmiddle" class="latex-formula"> form an arithmetic sequence. What is the sixth term of this sequence?
1 answer:
Answer:
Step-by-step explanation:
<h3>AP given</h3>
<h3>To find</h3>
<h3>Solution</h3>
Common difference
<u>Difference of first two</u>
d = (a -b) - (a + b) = -2b <u>Difference of second two</u>
<u>Difference of last two</u>
<u>Now comparing d:</u>
-2b = ab - (a - b) ab - a = - 3b a(1 - b) = 3b a = 3b/(1 - b) and
a/b - ab = -2b a(1/b - b) = -2b a = 2b²/(b² - 1) <u>Eliminating a:</u>
2b²/(b² - 1) = 3b/(1 - b) 2b/(b+1) = -3 2b = -3b - 3 5b = - 3 b = -3/5 <u>Finding a:</u>
a = 3b/(1 - b) = 3*(-3/5) *1/(1 - (-3/5)) = -9/5*5/8 = -9/8 <u>So the first term is:</u>
a + b = -3/5 - 9/8 = -24/40 - 45/40 = - 69/40 <u>Common difference:</u>
<u>The 6th term:</u>
a₆ = a₁ + 5d = -69/40 + 5*6/5 = -69/40 + 240/40 = 171/40 = 4 11/40
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Step-by-step explanation:
2ax−3<4x+5a
Step 1: Add -5a to both sides.
2ax−3+−5a<5a+4x+−5a
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Step 2: Add 3 to both sides.
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