The fourth and fifth terms of a sequence are $4$ & $5$ and $n^{t h}$ terms is given as $t_{n} = 2 t_{n - 1} - t_{n - 2}, n \geq 3$ then the sum to $2000$ terms is :

1999000

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

2000000

No worries! We‘ve got your back. Try BYJU‘S free classes today!

2001000

No worries! We‘ve got your back. Try BYJU‘S free classes today!

N o n e o f t h e s e

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A $1999000$
Given $t_{4} = 4, t_{5} = 5$
$t_{n} = 2 t_{n - 1} - t_{n - 2}, n \geq 3$
n=5
$t_{5} = 2 t_{4} - t_{3}$
$5 = 2 (4) - t_{3}$
$t_{3} = 8 - 5$
$t_{3} = 3$
n=4
$t_{4} = 2 t_{4} - t_{2}$
$4 = 2 (3) - t_{2}$
$t_{2} = 6 - 4$
$t_{2} = 2$
n=3
$t_{3} = 2 t_{2} - t_{1}$
$3 = 2 (2) - t_{1}$
$t_{1} = 1$
$1, 2, 3, 4, 5, \dots$ are in $A P$ whose first
term is 1 and 2000 th term is 2000
and total terms are 2000 .
Option (D).

Suggest Corrections

Similar questions

n th

t_{n} = 8 n + 3

20

n^{t h}

T_{n} = 2 n + 1

4

n^{t h}

t_{n} = 7 n - 9

100

n t h

t_{n} = n + 1

n^{t h}

t_{n} = \frac{1}{n + 1}

Join BYJU'S Learning Program