Question

if a,a1,a2......a10,b are in AP and are in a,g1,g2.......,g10,b are in GP and H is HM, between a and b,then

Answer 1

\[\frac{ a_1+a_2+..a_{10} }{ g_1g_{10} }+\frac{ a_2+a_3.. a_9}{ g_2g-9 }....\frac{ a_5+a_6 }{ g_5g_6 }\]

Answer 2

OPTIONS
a)10/h b)15/h c)30/h d)5/h

Answer 3

why does it always says kanwal32 is typing a reply when i am not

Answer 4

@hartnn any suggestions

Answer 5

@wio hlp

Answer 6

I think it might help if we rewrite the AP as follows:

a, a1, a2, a3, a4, a5, a6, a7, a8, a9, a10, b
a, a+d, a+2d, a+3d, a+4d, a+5d b-5d, b-4d, b-3d, b-2d, b-d, b


Same with GP also.

Answer 7

a1 + a2 + a3 + ... + a10 = 5(a+b)
a2 + a3 + a4 + ....+ a9 = 4(a+b)
a3 + a4 + a5 + ....+ a8 = 3(a+b)
a4 + a5 + a6 + a7 = 2(a+b)
a5 + a6 = (a+b)

Answer 8

@ganeshie8 nd @hartnn can u pls write the solution I will check it aftersome time cause I am studying chemistry (plss)

Answer 9

pls hlpp cause I am having an exam on sunday

Answer 10

a,g1,g2.......,g10,b are in GP
a, g1, g2, g3, g4, g5, g6, g7, g8, g9 , g10, b
a, ar, ar^2, ar^3, ar^4, ar^5, br^-5, br^-4, br^-3, br^-2, br^-1, b

g1*g10 = ar * br^-1 = ab
g2*g9 = ar^2 * br^-2 = ab
g3 * g8 = ar^3 * br^-3 = ab
g4 * g7 = ar^4 * br^-4 = ab
g5 * g6 = ar^5 * br^-5 = ab

\( \Large
\frac{ a_1+a_2+..a_{10} }{ g_1g_{10} }+\frac{ a_2+a_3.. a_9}{ g_2g-9 }....\frac{ a_5+a_6 }{ g_5g_6 } = \\ \Large
\frac{5(a+b)}{ab} + \frac{4(a+b)}{ab} + \frac{3(a+b)}{ab} + \frac{2(a+b)}{ab} + \frac{(a+b)}{ab} = \\ \Large
\frac{(a+b)}{ab}(5+4+3+2+1) = 15\frac{(a+b)}{ab} = \\
\text{Harmonic Mean of a and b} = \Large \frac{2ab}{a+b} = h \\ \Large
\frac{(a+b)}{ab} = \frac 2h.~~~ 15\frac{(a+b)}{ab} = 15 * \frac 2h = \frac{30}{h}
\)

Answer 11

@aum thnx for u r help

Answer 12

You are welcome.