Let a , b , c (in that order) are in arithmetic progression and ( a /2), b , ( c /4) (in that order) are in geometric progression. If b=2, then the value of (a4+b4+c4) is equal to

Question

Let a , b , c (in that order) are in arithmetic progression and ( a /2), b , ( c /4) (in that order) are in geometric progression. If b=2, then the value of (a4+b4+c4) is equal to (A) 256 (B) 272 (C) 284 (D) 296

Tardigrade Admin · Accepted Answer

Given a + c =2 b =4 and b 2=( ac /8) ⇒ ac =32 Now a4+c4=(a2+c2)2-2 a2 c2 =(( a + c )2-2 ac )2-2 a 2 c 2=(16-64)2-2(32)2=(48)2-2(32)2=(16)2(9-8) =256 Hence (a4+b4+c4)=256+16=272

Q. Let a,b,c (in that order) are in arithmetic progression and 2a​,b,4c​ (in that order) are in geometric progression. If b=2, then the value of (a4+b4+c4) is equal to

256

272

284

296

Given a+c=2b=4 and b2=8ac​⇒ac=32 Now a4+c4=(a2+c2)2−2a2c2 =((a+c)2−2ac)2−2a2c2=(16−64)2−2(32)2=(48)2−2(32)2=(16)2(9−8) =256 Hence (a4+b4+c4)=256+16=272

Q. Let $a, b, c$ (in that order) are in arithmetic progression and $\frac{a}{2}, b, \frac{c}{4}$ (in that order) are in geometric progression. If $b = 2$ , then the value of $(a^{4} + b^{4} + c^{4})$ is equal to