Answered

the 6th and 13th terms of a G.P is 24 and 3/16 respectively.find the sequence.

Answer :

vikaskumar0507
let the first term is a and common ratio is r
[tex] T_{6} [/tex] = a× [tex] r^{5} [/tex] = 24 --------------------(1)
[tex] T_{13} [/tex] = a× [tex] r ^{12} [/tex] = 3/16 ----------------------(2)
equation (1) ÷ (2)
24/(3/16) = 1/[tex] r^{7} [/tex]
128 = 1/[tex] r^{7} [/tex]
2 = 1/r
r = 1/2
put the value of r in equation (1) 
a×[tex] 1/2^{5} [/tex] = 24
a = 24*32 = 768
hence the sequence = 768, 384, 192, 96, 48, 24, 12, 6, 3, 3/2, 3/4............

Answer:

a=768

Step-by-step explanation:

let the first term is a and common ratio is r

= a×  = 24 --------------------(1)

= a×  = 3/16 ----------------------(2)

equation (1) ÷ (2)

24/(3/16) = 1/

128 = 1/

2 = 1/r

r = 1/2

put the value of r in equation (1)

a× = 24

a = 24*32 = 768

hence the sequence = 768, 384, 192, 96, 48, 24, 12, 6, 3, 3/2, 3/4............

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