I want check my answer
Q 1 : If the second term = 6 and fifteenth = 25 of sequence find the first term ?
$\displaystyle a_n = a_1 + (n-1)d$
$\displaystyle a_2 = a_1 + d$
$\displaystyle 6 = a_1 + d$
$\displaystyle a_{15} = a_1 + 14d$
$\displaystyle 25 = a_1 + 14d$
$\displaystyle 19 = 13d$
$\displaystyle d = \frac{19}{13}$
$\displaystyle a_1 = 6 - d = 6 - \frac{19}{13} = \frac{59}{13}$
No, because you haven't answered the question fully. You've been asked to find the first term a but you found the common difference d.
Your working seems fine though. Simply sub your value of d into one of your original equations to find a.
$\displaystyle U_2 = a + d = 6 $ (eq1)
$\displaystyle U_{15} = a + 14d = 25$ (eq2)
Rearrange eq1:
$\displaystyle d = 6-a$ (eq3)
sub eq3 into eq2
$\displaystyle a+14(6-a) = 25$
$\displaystyle -13a = -59$
$\displaystyle a = \frac{59}{13}$