Question

Sequences and series

Answer 1

If n arithmatic means are inserted between 20 and 80 such that first mean : last mean = 1:3 , find n

Answer 2

have you tried it?

Answer 3

Actually i have no idea . but let's still try

so,
\[\frac{ A _{1} }{ A _{n} }=\frac{ 1 }{ 3 }\]

Answer 4

20, a1,a2,.....an, 80

20 is 1st term
80 is last term

Answer 5

80 is (n+2)nd term

Answer 6

80th is n+2 term probably

Answer 7

yes
now make an equation with 20 and 80
n and d are unknown

Answer 8

so,

80 = 20 + (n+1)d
60=(n+1)d

Answer 9

Make an equation with 20 ?

Answer 10

yes
i was talking about that only.

now

Answer 11

a1 is the 2nd term
so,
a1 = 20 +d
an = 20+ nd

a1: an = 1:3

you have 4 equations, 4 unknowns
see if you can figure out n

Answer 12

okay ..

Answer 13

a1 = 20 +d
an = 20+ nd

add these

Answer 14

(a1+an) =
40 + d(1+n)

Answer 15

you already know value of (n+1)d

Answer 16

a1 +an is 100
a1 :an = 3

Answer 17

i mean a1/an = 1/3

Answer 18

a1 +3a1 = 100

a1 = 25
an = 75

Answer 19

d=5

Answer 20

a1 = 20 +d.........d= 5
an = 20+ nd........75 = 20 + 5n

Answer 21

75=20+5n
55=5n
n=11

Answer 22

\(\huge \checkmark\)

Answer 23

:) thanks