Sequences and series in functions questions

Question

a) Calculate the sum of the series: –396 – 308 – 220 – 132 – ... + 836.

b) Calculate the sum of the series 4 + 12 + 36 + ... + 2916.

c) Calculate the sum between and including the terms  and  of an arithmetic sequence with first term 543 and common difference –12.

d) The sum of a geometric sequence 2 – 6 + 18 – 54 + ... –  is –29 524. Find the number of terms.

Full steps would be greatly appreciated. Thank you!

Answer 1

d=88 = common difference for an arithmetic sequence

sn= n(a1+an)/2= half the average of 1st & last terms, all multiplied by number of terms

sn=n(-396+836)/2= 440n

836+396= 1232

1332/88= 14=n

s14 = 440(14)= 6160