the product of 5 terms of GP is 32.find the sum of 19 terms of AP if third term of GP=tenth term of AP?
I assume we are talking about the 1st terms of the sequences.
well, shucks, 32=2^5
1*2*4*8*16 too big
1/2 * 1 * 2 * 4 * 8 = 32
a= 1/2
r = 2
S19 = 19/2 (a + 18d)
but, a+9d = 2
so, 2a+18d = 4
so, a+18d = 4-a = 7/2
S19 = (19/2)(7/2) = 133/4