Question

28. If a, represents the nth term of an AP, prove that ap + ap+ 2q = 2ap+q​

Answer 1

ap + ap+ 2q = 2ap+q​

2(a+(p+q-1)d)= 2(a+(p+q-1)d)

LHS = RHS

Step-by-step explanation:

we have to prove that  ap + ap+ 2q = 2ap+q​

proof :

solving LHS and RHS seperately

we get

LHS : ap + ap+ 2q

a+ (p-1)d+a+(p+2q-1)d

= a+pd-d+a+pd+2qd-d

= 2a +2pd+2qd-2d

= 2(a+(p+q-1)d)...(1)

solving RHS :  2ap+q​

2(a+(p+q-1)d)....(2)

from equation (1) and (2)

2(a+(p+q-1)d)= 2(a+(p+q-1)d)

i.e ,

LHS = RHS

hence proved .

#Learn more:

If the pth term of an AP is a and th term of an AP is p ,prove that nth term is (p+q-n)

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