Sequences and Series question (1 Viewer)

[sinophile]

1. Find a and d of the AP in which T₆+T₈=44 and T₁₀+T₁₃=35

2. Find a and r of the GP in which T₂+T₃=4 and T₄+T₅=36.

 

[clintmyster]

1. Find a and d of the AP in which T₆+T₈=44 and T₁₀+T₁₃=35

2. Find a and r of the GP in which T₂+T₃=4 and T₄+T₅=36.

1)

T₆ = a + 5d
T₈ = a + 7d

T₆ + T₈
= a + 5d + a + 7d
= 2a + 12d = 44


T₁₀ = a + 9d
T₁₃ = a +12d

T₁₀ + T₁₃
= a + 9d + a + 12d
= 2a + 21d = 35
2a = 35 - 21d .............................................Rearranging above

2a + 12d = 44
(35 - 21d) + 12d = 44..................................(substituting 2a = 35 - 21d)
9d = -9
d = -1

2a = 35 - 21d
2a = 35 - 21(-1)............................................(substituting d = -1)
2a = 56
a = 28


2) is done in the same way but your using the formula T_n = ar^n-1
if you really want me to do it I will

 

[Timothy.Siu]

yeah 2nd ones the same basically,

ar+ar^2=4
ar^3+ar^4=36

ar(1+r)=4
ar^3(1+r)=36

(1+r)=4/ar
sub into the other one

4r^2=36
r=+-3
sub back into inital ones

r=3, a=1/3 r=-3, a=2/3

 

[sinophile]

Oh god it was that easy.. Thanks!