Question

The 12th term of an AP. is less than 5 to the 3 times of 5th term of same AP. and
4th term of AP. is 10. Find the series.​

Answer 1

Answer:

31

Solution:-

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

∴a

5

=3a

2

As we know that

a

n

=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.

∴a

12

=2a

6

+1

⇒a+11d=2(a+5d)+1

⇒a+11d=2a+10d+1

⇒a−d+1=0⟶(2)

From eq

n

(1)&(2), we have

⇒a−2a+1=0

⇒a=1

∴d=2a=2×1=2

∴a

16

=a+15d=1+15×2=1+30=31

Hence, the correct answer is 31.