Uahead(h r -hO), then show that he and dare in G.P. then show thatShe

1.	Uahead(h r -hO), then show that he and dare in G.P. then show thatShe the sum, P the product and the sum of reciprocals of a terms in a GPProve that PRSThe p q and terms of an AP are a respectively. Show thatrapb+ - 01 1 1are in AP, prove that a, care in AP10. If a
Answer» Given:The first term of the A.P. isa.The last term of the A.P. isl. To prove: The sum of thenth term from the beginning and thenth term from the end is (a + l). Let the common difference of the A.P. be 'd'. We know that thenth term of an A.P. is given by nthterm of the AP,Tn=a+ (n− 1)d ......(a) Also, we know that thenth term from the end of an A.P. is given by nthterm of the AP= [l- (n-1)d] ...... (b) Adding equations (a) and (b), we get a+ (n- 1)d+{l- (n- 1)d}=a+ (n- 1)d+l- (n- 1)d= a+l Therefore, it is proved that the sum of thenth term from the beginning and thenth term from the end is (a + l).

Uahead(h r -hO), then show that he and dare in G.P. then show thatShe the sum, P the product and the sum of reciprocals of a terms in a GPProve that PRSThe p q and terms of an AP are a respectively. Show thatrapb+ - 01 1 1are in AP, prove that a, care in AP10. If a

Answer»

Given:The first term of the A.P. isa.The last term of the A.P. isl.

To prove: The sum of thenth term from the beginning and thenth term from the end is (a + l).

Let the common difference of the A.P. be 'd'.

We know that thenth term of an A.P. is given by

nthterm of the AP,Tn=a+ (n− 1)d ......(a)

Also, we know that thenth term from the end of an A.P. is given by

nthterm of the AP= [l- (n-1)d] ...... (b)

Adding equations (a) and (b), we get

a+ (n- 1)d+{l- (n- 1)d}=a+ (n- 1)d+l- (n- 1)d= a+l

Therefore, it is proved that the sum of thenth term from the beginning and thenth term from the end is (a + l).