Question

is 51 a term of the AP 5, 8, 11, 14

Answer 1

a+(n-1)d here a=5 , d=3 & n=51
5+(51-1)3
5+50×3
5+150
155

therefore, 51 term is 155

Answer 2

Solution :

To check whether the value of 51 is a number of the series 5, 8, 11, 14 or not we first find the common difference of the series we get (8 – 5 = 3), (11 – 8 = 3).

Hence, it shows that the value of common difference is 3. Now to check if 51 is in the series or not put the value of a = 5 and d = 3 and 51 in the formula.

$T_{n}=a_{1}+(n-1) d$

$51=5+(n-1) 3$

$16=(n-1) 3$

$\frac{46}{3}=n-1$

As we can see, the value of n is in fraction now the value of the number of term should be positive non-fraction, non-decimal real number (excluding zero).  

Therefore, it shows that 51 is not a term of the series AP 5, 8, 11, 14.