Question

The fifth term of an A.P. is thrice the
second term and 12th term exceeds
twice the 6th term by 1. Find the
16th term.​

Answer 1

Answer:

Given that fifth term of an A.P. is thrice the second term.

∴a5=3a2

As we know that 

an=a+(n−1)d

∴a+4d=3(a+d)

⇒2a−d=0

⇒d=2a⟶(1)

Also given that twelfth term exceeds twice the 6th term by 1.

∴a12=2a6+1

⇒a+11d=2(a+5d)+1

⇒a+11d=2a+10d+1

⇒a−d+1=0⟶(2)

From eqn(1)&(2), we have

⇒a−2a+1=0

⇒a=1

∴d=2a=2×1=2

∴a16=a+15d=1+15×2=1+30=31