Question

Find the 12" term of a GP. whose 8" term is 192 and the common ratio is 2.
56
Class-X Mathematics
2
16
+1 torm​

Answer 1

Answer:

12th term of GP is 3072.

Step-by-step explanation:

Given that,

• 8th term is 192.
• Common ratio(r) is 2.

▶8th term is 192.

▶i.e. $a_8$ = 192

As we know that,

▶${\red{\sf{a_n = ar^{n - 1}}}}\:\bigstar$

▶${\sf{192 = a× (2)^{8 - 1}}}$

▶${\sf{192 = a × 2^7}}$

▶${\pink{\sf{a = \frac{192}{2^7}}}}$

Now, we need to find 12th of GP : We use the formula,

▶${\green{\sf{a_n = ar^{n - 1}} }}\:\bigstar$

▶${\sf{a_{12 }= \frac{192}{2^7} × 2^{12 - 1}}}$

▶${\sf{a_{12} = 192(2)^{11-7}}}$

▶${\sf{a_{12 }= 192(2)^4}}$

▶${\blue{\sf{a_{12} = 3072}}}$

Answer 2

Step-by-step explanation:

12th term of GP is 3072.

Given that,

8th term is 192.

Common ratio(r) is 2.

8th term is 192.

i.e. a_8a

As we know that,

${\red{\sf{a_n = ar^{n - 1}}}}$

${\sf{192 = a× (2)^{8 - 1}}}$

${\sf{192 = a × 2^7}}$

${\red{\sf{a = \frac{192}{2^7}}}}a$

Now, we need to find 12th of GP : We use the formula,

${\red{\sf{a_n = ar^{n - 1}} }}$

${\sf{a_{12} = 192(2)^{11-7}}}a$

${\sf{a_{12 }= 192(2)^4}}a$

${\red{\sf{a_{12} = 3072}}}a$

✔NOTE✔

Additional Info :

• Volume of cylinder = πr²h
• T.S.A of cylinder = 2πrh + 2πr²
• Volume of cone = ⅓ πr²h
• C.S.A of cone = πrl
• T.S.A of cone = πrl + πr²
• Volume of cuboid = l × b × h
• C.S.A of cuboid = 2(l + b)h
• T.S.A of cuboid = 2(lb + bh + lh)
• C.S.A of cube = 4a²
• T.S.A of cube = 6a²
• Volume of cube = a³
• Volume of sphere = 4/3πr³
• Surface area of sphere = 4πr²
• Volume of hemisphere = ⅔ πr³
• C.S.A of hemisphere = 2πr²
• T.S.A of hemisphere = 3πr²