can anybody tell me what is the next no. 120, 315, 300, 345, ?

Question

plz ans. the question. show how u can make the steps

Answer 1

120, 315, 300, 345, 720

120, 315, 300, 345 = 15( 8, 21, 20, 23)

Let Un = an³ + bn² + cn + d
U-2 = -8a + 4b - 2c + d = 8 .............. (1) Note the translation by 3 places back. This will be rectified by retranslating 2 forward at the solution by substituting (n - 3) for n
U-1 = -a + b - c + d = 21 ................. (2)
U0 = d = 20 .................... ................. (3)
U1 = a + b + c + d = 23 .................. (4)
Substitute (3) into (1), (2) and (4) and simplify
8a - 4b + 2c = 12
ie 4a - 2b + c = 6 ........... ................. (5)

a - b + c = -1 ................. .................. (6)

a + b + c = 3 ................. .................. (7)

(5) + 2*(7) 6a + 3c = 12
ie ............... 2a + c = 4 ................... (8)
(6) + (7) ... 2a + 2c = 2
ie ................ a + c = 1..................... (9)

(8) - (9) a = 3

So c = -2 and b = 2

So a = 3, b = 2, c = -2, d = 20

So Un+3 = 3n³ + 2n² - 2n + 20
So Un = 3(n - 3)³ + 2(n - 3)² - 2(n - 3) + 20
= 3(n³ - 9n² + 27n - 27) + 2(n² - 6n + 9) - 2n + 6 + 20
= 3n³ - 27n² + 81n - 81 + 2n² - 12n + 18 - 2n + 26
= 3n³ - 25n² + 67n - 37
So Tn = 15*Un

ie Tn = 45n³ - 375n² + 1005n - 555

Check on Excel
n ................ 1 ............ 2 ........... 3 ........... 4 ........... 5
Un .............. 8 .......... 21 ......... 20 ......... 23 ......... 48
Tn .......... 120 ......... 315 ....... 300 ....... 345 ....... 720

Addendum

if all that is important is the term then you can readuily and easily get it by method of differences. First set up the generations of differences

120 ...... 315 ...... 300 ...... 345
...... 195 ...... -15 ........ 45
............ -210 ....... 60
.................... 270

Then climb the right hand side of the difference set starting with the sme difference if you want to maintain the same order ... if you want to increase the order of Tn by 1 then start with a different number (any one you like in fact!!) So any answer is correct But the real question is to find Tn not the next number in the sequence.

120 ...... 315 ...... 300 ...... 345 ....... 720
...... 195 ...... -15 ........ 45 ....... 375
............ -210 ....... 60 ...... 330
.................... 270 ..... 270 ← start here and work back up by addition of number above left so 330 = 270 + 60, etc

Answer 2

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Answer 3

728

Answer 4

150. As in 120,315,300,345,150,375.

The sequence is 15^1,^13, ^(-1), ^3, .....

Answer 5

550?

Answer 6

there is no logical # in the sequence. You can insert any number you want and it will make as much sense as any other #.

Answer 7

120,315,300,345,390