Question

find the five terms of an ap whose sum is 12 1/2 and first and last term ratio is 2:3

Answer 1

given
s₅=12 1/2=25/2

$\frac{25}{2} = \frac{5}{2} [2a + (5 - 1)d] \\ 2a + 4d \: = 5 \\ 2(2a + 4d) = 2 \times 5 \\ 8d = 10 - 4a ...............(1)$
a₅= a +(5-1)d
a₅= a + 4d
now a/a₅ = 2/3
$\frac{a}{a + 4d} = \frac{2}{3 } \\ 3a = 2a + 8d \\ 8d = a \: ....................(2)$
equating (1) and (2)
a=10-4a
a =2
d = 2/8 = 1/4 [using (2)]
the first five terms of the AP are a a+d a+2d a+3d a+4d
the first five terms of the AP are 2
9/2
5/2
11/4
3