Find the nth term for the following sequences:
a. 2, 9, 18, 29, 42….. [4]
b. 10, 26, 58, 112, 194,….. [5]
Answers
Given : a. 2, 9, 18, 29, 42…..
b. 10, 26, 58, 112, 194,…..
To Find : Next term in sequence
Solution:
2
2 + 7 = 9
9 + 9 = 18
18 + 11 = 29
29 + 13 = 42
42 + 15 = 57
57 is next term
7 added in 2nd term , 9 added in 3rd term
Hence 2n+ 3 represent number being added in previous term
Tₙ = Tₙ₋₁ + 2n + 3 where T₁ = 2
10, 26, 58, 112, 194,
10
10 + 16 = 26
26 + 16 + 16 = 58
58 + 16 + 16 + 22 = 112
112 + 16 + 16 + 22 + 28 = 194
194 + 16 + 16 + 22 + 28 + 34 = 310
310 is next term
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