Question

the sum of first 20 terms of a gp is 1025 times the sum of 10 terms of same gp.find the common ratio
द सम आफ फर्स्ट न टर्म्स ऑफ़ अ जीपीएस 1025 टाइम्स द सम ऑफ द टाइम्स ऑफ जीपी फाइंड द कॉमन रेशों ​

Answer 1

Answer:

tttttt the two compound words for example keyhole is the height of the two compound

Answer 2

Step-by-step explanation:

S20 = a ( r^20 - 1) / ( r - 1)

S10 = a ( r^10 - 1) / (r - 1)

a *{(r^20 - 1) / (r - 1)} = 244 * {a*( r^10 - 1)} / (r - 1)

….( given)

Or, (r^20 - 1) = 244*(r^10 - 1)

Or, ( r^10 + 1)*(r^10 - 1) = 244* (r^10 - 1)

Or, ( r^10 + 1) = 244

Or, r^10 = 244 - 1 = 243

So, 10* log r = log 243 = 2.3856

Or, log r = (1/ 10)* (2.3856) = 0.23856

Or, rounding off, log r = 0.2386

Therefore, r = antilog 0.2386

r = 1.732

So, the common ratio of the GP is 1.732 or, √3 Answer

Check:

S10 = a* (r^10 - 1) / (r- 1)

= a* ( 1.732^10 - 1) / (1.732 - 1)

= a*( 243- 1) / 0.732 ….(1)

S20 = a*( 1.732^20 - 1) / ( 1.732 - 1)

= a*[{( 1.732^10)^2} - 1] / 0.732

= a* {( 243*243) - 1} / 0.732 …. (2)

So, S20 / S10 = a* {(243*243) - 1) / a*(243 - 1)

= (243*243) - 1 / 242 =(59049 - 1) / 242

= 59048 / 242 = 244 ✓