Calculus- confused please help

Question

Find A

Find B

Answer 1

The sequence 8, 12, 16, ..., 64 seems to be an arithmetic progression with difference 4, so the general term will be t_n = c + 4n. When n = 1, c + 4 = 8, so c = 4. When t_n = 64, we have 4n = 64 - 4 = 60, so n = 15.

So the answers are A = 15, B = 4 + 4n

Answer 2

Meant to mention that the formula for the sum of an arithmetic series (finite) is given by:

S_n = n(a₁+a_n) / 2 => number of terms times average of 1st and last,

For this problem S₁₅ = 15(8+64)/2 = 15(36) = 540.

Answer 3

The series is arithmetic with a₁ = 8 and d = 4

B = 8 + (n - 1)4

64 = 8 + 4(n - 1)

56 = 4n - 1

57.= 4n

14 = n

A = 14