Question

If 5,12,19 are in a series then which number can't be included in the series
a)724
b)656
c)810
d)915

Answer 1

Answer:

$\bold\red{(a)724}$

Step-by-step explanation:

The given series 5,12,19...... is in AP.

Here,

first term , a = 5 and,

common difference, d = 12-5 = 7

Now,

we know that in an AP,

nth term = a +(n-1)d

So, for the given AP,

nth term = 5+ 7(n-1)

Lets, check the given numbers.

a) 724 = 5 + 7(n-1)

=> 7(n-1) = 719

=> n-1 = 719/7

=> n = (719+7)/7

=> n = 726/7

But, its fraction, which can't be possible.

So, it's not in the series.

b) 656 = 5 +7(n-1)

=> 7(n-1) = 651

=> n-1 = 651/7 = 93

=> n = 93+1 = 94

Therefore, it is in the series.

Similarly,

(c)810 and (d)915

are also in the given series.

Hence, (a)724 is the correct answer which is not in the series.