Question

the sum of the third and fourth terms of a GP be 60 and that of the 6th and 7th terms be 480 find the the 10th term of the GP​

Answer 1

Answer:

third term =ar²

fourth term =ar³

sixth term =ar⁵

seventh term=ar⁶

now ,

ar²+ar³=60------->(1)

ar⁵+ar⁶=480------->(2)

(2)/(1)

a(r⁵+r⁶) 480

------------. = ------------

a(r²+r³) 60

a is cancelled and r⁵ is is taken common in numerator and r² is taken common in denominator

r⁵(1+r)

----------. =. 8

r²(1+r)

now (1+r) is cancelled and r⁵ is divided by r² giving r³

r³=8

r³=2³

r=2

putting value of r in eqñ (1) ,

a 2²+a2³=60

4a+8a=60

12a=60

a=5

now ,the 10th term of the GP

ar⁹= 5*2⁹

5*512

2560

done !! hope you like the answer

Answer 2

Answer:

Value of 10th term is 2560.

Hope you understood the explanation☺️