term of arithmetic and geometric sequences

Question

Find the sum of this series . Find the value of (n) first then find the sum of the (n) terms

Answer 1

r= -3 = common ratio of a geometric series

an= 5r^(n-1)

295245 = an = 5r^(n-1)

r^(n-1) = 295245/5 = 59049

3^(n-1) = 59049

3^10 = 59049

n-1 = 10

n = 11

a11=295245

sn = a1(r^n-1)/(r-1)

= 5(3^11-1)/(3-1)

= (5/2)(295244)

= 738,110