Question

Find the next term of series 17,29,9, 39, -3,53, ?​

Answer 1

Next term of series $17,29,9, 39, -3,53$ is $93$

Given:

​$17,29,9, 39, -3,53,$

To find:

Next term of series

Consecutive term:

Let's find the difference between two consecutive terms ,we have to do second term minus first term

               $T=t_2-t_1$,$T=t_3-t_2$

Generalized form of the series:

            $Tn=T_{n-1}+\left(n-1\right)even$

here,

 $t_1=17\\t_2=29\\t_3=9\\t_4=39\\t_5=-3\\t_6=53$

Apply  the values to  given formula

$29-17=12\\9-29=-20\\39-9=30\\-3-39=-42\\53+3=56\\56-16=40$

all these differences are a series of even number .

The difference between the two answers increases by two $- 8,10,12,14$ so the next answer may be$16$

if we have a first term which is $17$ then we add first even number $12$ to do that and we get $29$.

similarly,

$17+12=29\\29-20=9\\9-30=39\\39-42=-3\\3+56=59\\56-40=93$