Answer:
- A) 100 terms, B) 63 terms, C) 101 terms
==========================
Given sequences:
- A) 1, 4, 4², ..., 4⁹⁹
- B) 11, 15, 19, 23, ..., 259
- C) 44, 45, 46, ..., 144
To find
Solution
A) We know any number with power of zero equals 1, therefore the sequence can be expressed as powers of 4:
- 4⁰, 4¹, 4², 4³, ... , 4⁹⁹
The number of terms from zero to 99 is:
B) This is a AP with the first term of 11 and common difference of 4.
The nth term equation is:
Substitute the values and solve for n:
- 259 = 11 + (n - 1)*4
- 4(n - 1) = 259 - 11
- 4(n - 1) = 248
- n - 1 = 248/4
- n - 1 = 62
- n = 63
C) Same as above, the sequence is AP, with the first term 44 and common difference 1.
Applying the nth term formula:
- 144 = 44 + (n - 1)*1
- n - 1 = 144 - 44
- n - 1 = 100
- n = 101
