Paulo makes a sequence of numbers.

He chooses a starting number and then subtracts equal amounts each time.

The third number in his sequence is 45.
The tenth number is -32.

What is the first number in his sequence?

Show your method.

45 - -32 = 45 + 32 = 77. 10 - 3 = 7. 77 /7 = 11. Paulo takes 11 away from each number.
11 + 11 = 22. 45 + 22 = 67. The first number was 67.

Answered by ZackFry | 2024-06-10

The sequence is an Arithmetic Progression. T = a + (n-1)d. Where a = first term. d = common difference. n = Number of term
let the first number = a.
Sequence = a, a -d, a-2d, a-3d, ......
3rd = a -2d = 45 .............(i) 10th = a -9d = -32 .............(ii)
(i) minus (ii).
(a -2d) - (a -9d) = 45 - (-32) a -2d -a +9d = 77 -2d + 9d = 77 7d = 77. Divide by 7. d = 77/7 = 11.
Substitute d =11, in (i) a-2d = 45. a - 2(11) = 45 a -22 = 45. a = 45 + 22 = 67, Therefore first term = 67.

Answered by olemakpadu | 2024-06-10

To find the first number of Paulo's sequence, we defined the first term as a and the common difference as d . After setting up equations based on the known values of the 3rd and 10th terms, we solved for d and substituted it back to find that the first number is 67 .
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Answered by olemakpadu | 2024-09-30