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
Step-by-step 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
