Question

If (a - b)², (a² +b²)

are the first two
terms of an AP, then find the next term.​

Answer 1

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

Answer 2

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:-

• The nth term of an AP = an=a+(n-1)d
• a = First term
• d = Common difference
• n = Number of terms