GEOMETRIC PROGRESSION K1

 

In a G.P. the ratio of 8^th term and 6^th term is 4. If the sum of 2nd term and 4^th term is 240, Find the

(a)         Common ratio

(b)        The 1^st term.

 

Solution

 

G_n =G₁r^n-1.

 

G₈ =G₁r^8-1

 

G₈ =G₁r⁷

G₆ =G₁r^6-1.

G₆ =G₁r⁵.

 

^G6/_G8 =4

G₁r⁷/ G₁r⁵.=4

r⁷/r⁵=4       [G1 cancels out]

r^7-5=4

r²=4

√r²=√4   root sign

r = 2.

 

Hence the common ratio is 2

 

Now the 2^nd  term plus 4^th term is 240

G_n =G₁r^n-1.

 

G₉ =G₁r^9-1

G₉ =G₁r⁸

 

G₁₀ =G₁r^10-1

G₁₀ =G₁r⁹

 

G₁r + G₁r³ = 240

G₁(r  +  r³) = 240

G₁(2 +  2³) = 240       [since r=2]

G₁(2 +  8) = 240    

10G₁= 240    

Now G₁= ²⁴⁰/₁₀ = 24    

 

Hence the st term is 24.     

TRY THIS...................

In a G.P. the ratio of 7^th term and 4^th term is 27. If the sum of 3rd term and 5^th term is 180, Find the

(a)         Common ratio

(b)        The 1^st term.

(c)          The 8^th term