Question

The sum of the second and third term is6 and the sum of the third and fourth is -12.Find,
_The common ratio
_The sum of number of consecutive terms of an arithmetic progression is 19,1/2.The first term is 16,1/2 and the common difference is -3.Find the number of terms.

Answer 1

ar+ar^2 = 6
ar^2 + ar^3 = -12
now solve for r

Sn = n/2 (2a + (n-1)d) so you have
n/2 (2(16 1/2) + (n-1)(-3)) = 19 1/2
I suspect a typo

Answer 2

6.6