Construct a difference table to predict the next term of the sequence
-1,4,21,53,103,174,

391

Step-by-step explanation:

Given sequence: -1,4,21,53,103,174,269

Lets find the pattern of sequence to predict the next term.

Finding difference between each term till we find common difference.

1st term (-1)= 4-(-1)= 5    

                                   17-5= 12  

2nd term (4)=21-4= 17                            15-12= 3

                                    32-17= 15

3rd term(21)= 53-21= 32                          18-15= 3

                                      50-32= 18

4th term (53) = 103-53= 50                     21-18= 3

                                       71-50= 21

5th term (103)= 174-103= 71                     24-21= 3

                                       95-71= 24

6th term(174) = 269-174= 95

We can observe common difference of 3 and we have 7th term as 269, now we need to find 8th term in the sequence

starting with common difference, we will add numbers from back of array to get the 8th term.

⇒

⇒

∴

Hence, the next term of the sequence will be 391.

the image of (6, 9) under a dilation is (4, 6). the scale factor is