Can you find the next two terms?

The general term for this sequence is 2*3^n - 1.

So t5 = 2*3^5 - 1 = 2*243 - 1 = 485.

And t6 = 2*3^6 - 1 = 2*729 - 1 = 1457

T 1 = 1

T 2 = 5 = 3 x 1 + 2 = 3 + 2 = 5 = 3 x T1 + 2

T 3 = 17 = 3 x 5 + 2 = 15 + 2 = 17 = 3 x T2 + 2

T 4 = 53 = 3 x 17 + 2 = 51 + 2 = 53 = 3 x T3 + 2

T 5 = 161 = 3 x 53 + 2 = 159 + 2 = 161 = 3 x T4 + 2

T 6 = 161 = 3 x 161+ 2 = 483 + 2 = 485 = 3 x T5 + 2

T 7 = 161 = 3 x 485 + 2 = 1455+ 2 = 1457 = 3 x T6 + 2

T 8 = 161 = 3 x 1457+ 2 = 4371 + 2 = 4373 = 3 x T7 + 2

The Formula for the series Tn = { 3 x T(n-1) } + 2

Where Tn in the n th term and T (n-1) is the previous term of the series

So by using this formula you can find any term in this series, but you must work for each term

If you or your frind is competent in EXCEL , you can apply the formula and see how the series is going up

For example by excel the series is this one

1

5

17

53

161

485

1457

4373

13121

39365

118097

354293

1062881

3188645

9565937

28697813

86093441

258280325

774840977

2324522933

6973568801

The given terms increase by 4, 12, 36, 108...

ie the increase is multiplied by 3 each time.

The next increases are 3*108 = 324 and 3*324 = 972

161 + 324 = 485 <<<

485 + 972 = 1457<<<

3x1 = 3 [+2] = 5

3x5 = 15 [+2] = 17

3x17 = 51 [+2] = 53

3x53 = 159 [+2] = 161

3x161 = 483 [+2] = 485

3x485 = 1455 [+2] = 1457