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

See the attachment for detail solution
Hope it will help you

Answer 2

Answer:

16th term is 16

Step-by-step explanation:

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

To find : The 16th term.

Solution : The general form of an Arithmetic Progression is

a, a+d, a+2d, a+3d and so on.

Thus, nth term of an AP series is $T_n = a + (n - 1) d$

where $T_n$ = nth term , a = first term , d= common difference

Now,

Situation 1 - The fifth term of an A. P. is thrice the second term

$T_5=3\times T_2$

$\Rightarrow(a+4d)=3\times (a+d)$

$\Rightarrow a+4d=3a+3d$

$\Rightarrow d=2a$ ......[1]

Situation 2- 12th term exceeds twice the 6th term by 1.

$T_{12}=2\times T_6+1$

$\Rightarrow(a+11d)=2\times (a+5d)+1$

$\Rightarrow(a+11d)=2a+10d+1$

$\Rightarrow d=a+1$ .......[2]

From equation [1] put value of d in equation [2]

$d=a+1$

$\Rightarrow 2a=a+1$

$\Rightarrow a=1$

Now, put value of a in d we get,

$d=a+1$

$\Rightarrow d=1+1=2$

Therefore, a=1 and d=2

So, 16th term

$T_{16}=a+15d$

$T_{16}=1+15(1)$

$T_{16}=16$

Hence, 16th term is 16.