Question

 if tn denotes the nth term of the series 2+3+6+11+18+...........,then find t50.

Answer 1

"Difference of the terms of this series is in A.P.

2+1 = 3,

2+1+3 = 6,

2+1+3+5= 11,

2+1+3+5+7 = 18 and so on.

Sn = n/2[ 2a + ( n - 1 ) d ]

Here a = first term = 1 , n = number of term = 49 and d = common difference = 2 , So

Sn = 49/2[ 2( 1 ) + ( 49 - 1 ) 2 ] = 49 [ 1 + ( 49 - 1 ) ] = 492

Hence, Sum of 49 terms of series 1,3,5,7,9,11,.. = 492

Now, to get the T50 term.. add 2+ sum of the 1+3+5+7+..+97

T50 of series 2 + 3 + 6 + 11 + 18+....... = 2 + 492 = 2 + 2401 = 2403

"

Answer 2

Answer:

t50=2403

Step-by-step explanation:

2+0²,2+1²,2+2²,2+3²,2+4²

tn= (n-1)²+2

t50= (50-1)²+2

t50= (49)²+2

t50=2403