Answer:
a. The first four terms and the 10th term are 6, 12, 22, 36, ......., 204
b. The first four terms and the 10th term are 0, 9, 24, 45, ......., 297
c. The first four terms and the 10th term are 4, -5, -20, -41, ......., -293
d. The first four terms and the 10th term are -1, 11, 31, 59, ......., 395
Explanation:
a.
∵ T(n) = 2n² + 4 is the rule of the sequence, where
- n is the position of the number in the sequence
∴ For the first term, n = 1
→ Substitute n by 1 in the rule above to find T(1)
∵ T(1) = 2(1)² + 4 = 2(1) + 4 = 2 + 4
∴ T(1) = 6
→ For the second term, n = 2
∵ T(2) = 2(2)² + 4 = 2(4) + 4 = 8 + 4
∴ T(2) = 12
→ For the third term, n = 3
∵ T(3) = 2(3)² + 4 = 2(9) + 4 = 18 + 4
∴ T(3) = 22
→ For the fourth term, n = 4
∵ T(4) = 2(4)² + 4 = 2(16) + 4 = 32 + 4
∴ T(4) = 36
→ For the tenth term, n = 10
∵ T(10) = 2(10)² + 4 = 2(100) + 4 = 200 + 4
∴ T(10) = 204
The first four terms and the 10th term are 6, 12, 22, 36, ......., 204
b.
∵ T(n) = 3n² - 3 is the rule of the sequence
→ For the first term, n = 1
∵ T(1) = 3(1)² - 3 = 3(1) - 3 = 3 - 3
∴ T(1) = 0
→ For the second term, n = 2
∵ T(2) = 3(2)² - 3 = 3(4) - 3 = 12 - 3
∴ T(2) = 9
→ For the third term, n = 3
∵ T(3) = 3(3)² - 3 = 3(9) - 3 = 27 - 3
∴ T(3) = 24
→ For the fourth term, n = 4
∵ T(4) = 3(4)² - 3 = 3(16) - 3 = 48 - 3
∴ T(4) = 45
→ For the tenth term, n = 10
∵ T(10) = 3(10)² - 3 = 3(100) - 3 = 300 - 3
∴ T(10) = 297
The first four terms and the 10th term are 0, 9, 24, 45, ......., 297
c.
∵ T(n) = -3n² + 7 is the rule of the sequence
→ For the first term, n = 1
∵ T(1) = -3(1)² + 7 = -3(1) + 7 = -3 + 7
∴ T(1) = 4
→ For the second term, n = 2
∵ T(2) = -3(2)² + 7 = -3(4) + 7 = -12 + 7
∴ T(2) = -5
→ For the third term, n = 3
∵ T(3) = -3(3)² + 7 = -3(9) + 7 = -27 + 7
∴ T(3) = -20
→ For the fourth term, n = 4
∵ T(4) = -3(4)² +7 = -3(16) + 7 = -48 + 7
∴ T(4) = -41
→ For the tenth term, n = 10
∵ T(10) = -3(10)² + 7 = -3(100) + 7 = -300 + 7
∴ T(10) = -293
The first four terms and the 10th term are 4, -5, -20, -41, ......., -293
d.
∵ T(n) = 4n² - 5 is the rule of the sequence
→ For the first term, n = 1
∵ T(1) = 4(1)² - 5 = 4(1) - 5 = 4 - 5
∴ T(1) = -1
→ For the second term, n = 2
∵ T(2) = 4(2)² - 5 = 4(4) - 5 = 16 - 5
∴ T(2) = 11
→ For the third term, n = 3
∵ T(3) = 4(3)² - 5 = 4(9) - 5 = 36 - 5
∴ T(3) = 31
→ For the fourth term, n = 4
∵ T(4) = 4(4)² - 5 = 4(16) - 5 = 64 - 5
∴ T(4) = 59
→ For the tenth term, n = 10
∵ T(10) = 4(10)² - 5 = 4(100) - 5 = 400 - 5
∴ T(10) = 395
The first four terms and the 10th term are -1, 11, 31, 59, ......., 395