Question

The fifth term of an A.P exceeds twice the second term by 1.The tenth term exceeds twice the fourth term by 3.
Find:1.the first term.
2.the common difference.
3.the sum of first twenty five terms.

Answer 1

Xn = a + (n-1)d

X5 = a + 4 d

X5 - 1 = 2 [ a + d ]

X10 - 3 = 2 [ a + 3 d ]
but X10 = a+9d

so

a + 4 d - 1 = 2 a + 2 d
a = 2 d - 1

a + 9 d - 3 = 2 a + 6 d
a = 3 d -3

combine
3 d - 3 = 2 d - 1
d = 4

You take it from there.