In an A.P. if Tₚ = q and Tq = p, then find the rth term.
Please solve this problem
Answers
Formula:
We know that
nth term of the AP is Tn = a+(n-1)d
Where, a = First term
d = Common difference
n = number of terms
Now,
Given that
pth term of the A.P. = Tp = q
⇛a + (p-1)d = q
⇛(p-1)d = q - a
⇛d = (q-a)/(p-1) →→→→(i)
and
qth term of the A.P. = Tq = p
⇛a + (q-1) d = p
⇛ (q-1)d = p-a
⇛ d = (p-a)/(q-1) →→→→(ii)
From Eqn(i) and Eqn(ii)
⇛(q-a)/(p-1) = (p-a)/(q-1)
On applying cross multiplication then
⇛(q-a)×(q-1) = (p-a)×(p-1)
⇛q²-q-aq+a = p²-p-ap+a
⇛q²-q-aq = p²-p-ap
⇛ap-aq = p²-p+q-q²
⇛a(p-q) = (p²-q²)-(p-q)
⇛a(p-q) = (p+q)(p-q)-(p-q)
⇛ a(p-q) = (p-q){(p+q)-1}
On cancelling (p-q) both sides then
⇛a = (p+q-1) →→→→Eqn(iii)
On Substituting the value of a in Eqn(ii) then
⇛ d = [p-(p+q-1)]/(q-1)
⇛d = (p-p-q+1)/(q-1)
⇛d = (-q+1)/(q-1)
⇛d = -(q-1)/(q-1)
⇛d = -1
We have,
a = p+q-1 and d = -1
Now, rth term of the AP
⇛ Tr = a + (r-1)d
⇛Tr = (p+q-1)+(r-1)(-1)
⇛ Tr = p+q-1+(-r+1)
⇛ Tr = p+q-1-r+1
⇛ Tr = p+q-r
Therefore, Tr = p+q-r
Answer: rth term of the given A.P. is p+q-r
Answer:
rth=q+p+qxp
Step-by-step explanation:
rth= 3 of the T and Tq added together and joined.
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Answer:
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Step-by-step explanation:
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Answers
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Step-by-step explanation:
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Answer:
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Step-by-step explanation:
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The length of the garden is 17 feet; its width is 7 feet.
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Answers
Answer:
Step-by-step explanation:
write a proportion and cross multiply to solve for x
[tex]\frac{60}{100} = \frac{x}{1280}[/tex]
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Answers
Answer:
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Step-by-step explanation:
x is the grams of water
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Answer:
1188
Step-by-step explanation:
Start with the part and whole proportion
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multiply the one by 12 and 100 by 12
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now subtract 12 from 1200
then you get 1188.
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Step-by-step explanation:
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Step-by-step explanation:
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Step-by-step explanation:
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Using proportions, it is found that:
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Answers
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_____
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Answers
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Answer:
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Answers
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Hi there, I hope you understand my answer and that it is correct :)
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____________________________________________________________
Next We subtract the answer, which we got to be 1,700 from 1266.
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____________________________________________________________
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Step-by-step explanation:
would help a lot if you show the picture or describe it very well.
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Bidmass
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glad to help
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It is 4pi/7, or b. Just want to help ;)
Pls HELPPPPPP!! the answer
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( -2,1 )
Hope it helps
Have a good day!!
:))))))
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Answers
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Subtract:
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Answers
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Answers
Answer:
SAS similarity
Step-by-step explanation:
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