Question

The eighth term of a geometric progression is 32 and the fourth term is 2. Find the first term and the positive value of the common ratio
b) find the sum to infinity of a geometric progression whose first term is 5 and second term is -4
c) The nth term of an arithmetic progression is 3n +7. Find the sum of the first 40 terms

Answer 1

Anyone to help me solve this please

Answer 2

there are 4 terms from the 4th to the 8th, so r^4 = 32/2 = 16
r = ±2

if a1 = 5 and a2 = -4, then r = -4/5
S = a/(1-r) = 5/(1 + 4/5) = 25/9

if the nth term is 3n+7, then
a = 10 and d = 3
S40 = 40/2 (2*10 + 39*3) = 2740