If (a - b)², (a² +b²)
are the first two
terms of an AP, then find the next term.
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If (a - b)², (a² +b²)
are the first two
terms of an AP, then find the next term.
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Answer:
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Step-by-step explanation:
so here for a certain ap
t1=a=(a - b)²
expanding it we get
a square+b square-2ab
thus our t1=a=a square+b square-2ab
moreover here t2=(a² +b²)
so thus then
d=t2-t1
=a² +b²-(a square+b square-2ab)
=a² +b²-a square-b square+2ab
ie nothing but d=2ab
so as it is an ap common difference between each of the terms would be constant
hence d=2ab
so to find third term ie t3
applying
t3=t2+d
=a² +b²+2ab
=(a+b) square
hence our next term is (a+b) square
Step-by-step explanation:
Given :-
(a - b)², (a² +b²) are the first two terms of an AP.
To find:-
Find the next term.?
Solution :-
Given that :
(a - b)², (a² +b²) are the first two terms of an AP.
a1 = (a-b)² = a²-2ab+b²
a2 = a²+b²
We know that
Common difference (d) = a2-a1
=> d = (a²+b²)-(a-b)²
=> d = (a²+b²)-(a²-2ab+b²)
=> d = a²+b²-a²+2ab-b²
=> d = (a²-a²)+(b²-b²)+(2ab)
=> d = 0+0+2ab
=> d = 2ab
Therefore,Common difference = 2ab
We know that
The nth term of an AP = an=a+(n-1)d
The next term of the AP = a3
=> a3 = a+(3-1)d
=> a3 = a+2d
On Substituting the values of a and f in the above formula then
=>a3 = (a-b)²+2(2ab)
=> a3 = a²-2ab+b²+4ab
=>a3 = a²+2ab+b²
=>a3 = (a+b)²
Answer:-
The next term is (a+b)²
Used formulae:-