The second one:
2*[1-(-3)^n] / [1 -(-3)]=-29,524
Solve for n:
1/2 (1 - (-3)^n) = -29524
Multiply both sides by 2:
1 - (-3)^n = -59048
Subtract 1 from both sides:
-(-3)^n = -59049
Multiply both sides by -1:
(-3)^n = 59049
Take the logarithm of both sides, ignoring the - sign:
Log(59,049)/ Log(3)
Answer: n = 10
P.S. Regarless of -3, you can still take the positive log of both sides. It will still give you an accurate n.
The first one:
I shall consider the 16th term as the 1st. term =543
53 - 16 + 1 =38 number of terms.
Common difference =-12
Sum =n/2[2a + (n -1)d]
Sum =38/2[2*543 + (38 - 1)*(-12)]
Sum = 19[1,086 + (-444)]
Sum = 19[642]
Sum =12,198