Write the statement for the problem in mathematical language. Use x for the tens digit and y for the unit digits in the two digit numbers. Find the two-digit number which is 2 times the sum of its digits

  18

Step-by-step explanation:

A two-digit number (xy) will have the value 10x+y. The sum of its digits is x+y.

You want ...

  10x +y = 2(x +y)

  1 ≤ x ≤ 9

  0 ≤ y ≤ 9

The equation can be simplified to ...

  8x = y

The only single-digit values for x and y that satisfy the requirements are ...

  x = 1, y = 8

The two-digit number of interest is 18.

Check

Its sum of digits is 1+8 = 9. 2×9 = 18.

Comment on the relationship in the problem

Many of us learned our multiplication tables for 9s by remembering that the sum of digits of 9n was 9, and that the leading digit of the product was n-1.

see explanation

step-by-step explanation:

since the sequence is geometric there is a common ratio r between consecutive terms, that is

r = 4 ÷ - 2 = - 2

r = - 8 ÷ 4 = - 2

r = 16 ÷ 8 = - 2

the next term - 13 must be incorrect as it should be - 32 for the sequence to be geometric.

the first 4 terms are therefore geometric with common ratio r = - 2