[tex]10=2d[/tex]
Given:
The sum of the first three terms of a sequence Is 42.
The fourth term is 24.
To find:
The u₁ and the common difference
Step-by-step explanation:
nth term of a sequence is
[tex]u_n=u_1+(n-1)d[/tex]
where, u₁ is first term and d is common difference.
4th term is 24.
[tex]u_4=u_1+(4-1)d[/tex]
[tex]24=u_1+3d[/tex] ...(i)
Sum of nth term of an AP is
[tex]S_n=\dfrac{n}{2}[2u_1+(n-1)d][/tex]
Sum of first three terms is 42.
[tex]S_3=\dfrac{3}{2}[2u_1+(3-1)d][/tex]
[tex]42=\dfrac{3}{2}[2u_1+2d][/tex]
Divide both sides by 3.
[tex]14=u_1+d[/tex] ...(ii)
On subtract (ii) from (i), we get
[tex]10=2d[/tex]
[tex]5=d[/tex]
Put d=5 in equation (ii).
[tex]14=u_1+5[/tex]
[tex]14-5=u_1[/tex]
[tex]9=u_1[/tex]
Therefore, the first term is [tex]u_1=9[/tex] and common difference is [tex]d=5[/tex] .
