Question

How many terms of an ap 1,4,7are needed to make the sum 51

Answer 1

t1 = 1
t2= 4
d = t2-t1
=4-1
=3.
it is given that Sn=51
$sn = \frac{n}{2} (2a + (n - 1)d) \\ 51 \times 2 = n(2 \times 1 + (n - 1)3) \\ 102 = n(2 + 3n - 3) \\ 102 = 2n + 3 {n}^{2} - 3n \\ 102 = 3 {n}^{2} - n \\ 3 {n}^{2} - n - 102 = 0$
comparing with quadratic equation
ax^2+bx+c=0
a=3
B=-1
c=-102
$x = \frac{ -( - 1) + - \sqrt{ {( - 1)}^{2} } - 4 \times 3 - 102}{2 \times 3} \\ x = \frac{ 1 + - \sqrt{1225} }{6} \\ x = 1 + 35 \div 6 \: or \: x = 1 - 35 \div 6 \\ x = 6 \: or \: x = \frac{ - 17}{3}$
6 terms are needed to make the sum 51.
hope this helps you:-))))
don't forget to do it brainleist.