Arithmetic progression

[charred estuary]

4th one

[tawdry turret]

,rotate

[tawdry turret]

1st sequence: T(n) = 4n - 3
2nd sequence: T(n) = 3n - 2
4n - 3 = 3n - 2
n = 1
hence only 1 identical term when n = 1

[thin relic]

Didn't it mean identical terms even if they don't have the same n?

For example 4(4) - 3 = 3(5) - 2

[tawdry turret]

yea I just realized the mistake

[tawdry turret]

1st sequence: T(n) = 4n - 3
2nd sequence: T(n) = 3n - 2
4n - 3 = 197 -> n = 50
3n - 2 = 196 -> n = 66
4m - 3 = 3n - 2, 1<=m<=50, 1<=n<=66
m = (3n + 1)/4
n = 1 -> m = 1
n = 5 -> m = 4
n = 9 -> m = 7
...
n = 4k - 3
4k - 3 = 66
k = 17.25 ≈ 17
check:
n = 4(17) - 3 = 65
n = 65 -> m = (3(65) + 1)/4 = 49 (<=50)
hence total number of identical terms = 17

[charred estuary]

the books says , ans is 16