Question

find the nth term of series:
rn
10, 23,60,169,494.......
rn
(the second time difference between nos. forms a GP )

Answer 1

✔️✔️we know that the n^th term:-
= x.3^n-1 + y.n + z

✔️here 3^n-1 because the common ration is 3, and it is n-1 and not n for reasons.....

✔️Put n = 1,2 and 3 to get three equations: -

10 = x + y + z ➖➖➖➖➖[1]

23 = 3x + 2y + z ➖➖➖➖➖[2]

60 = 9x + 3y + z ➖➖➖➖➖[3]

✔️Subtract eqn [1] from [2] ....

✔️ we get :-

2x + y = 13, and 2 from 3 to get 6x +?y = 37.

✔️Solve to find that question mark:-

x= 6, y = 1.

✔️ Put it in eqn 1 to get z = 3. 

✔️So the n^th term of the series is:-
6.3^n-1+ n + 3....