Answer:
S₈ = 296
Step-by-step explanation:
Given: 2 + 12 + 22 + 32 + .... + (10n - 8) = [tex]$5n^2 - 3n $[/tex]
To prove [tex]$ S_8 $[/tex] is true, substitute [tex]$ n = 8 $[/tex] and compare LHS and RHS
n = 8:
[tex]10n - 8 = 10(8) - 8[/tex]
[tex]$ \implies 72 $[/tex]
[tex]$ \therefore LHS = 2 + 12 + 22 + 32 + 42 + 52 + 62 + 72 $[/tex]
[tex]$ = 296 $[/tex]
Now, Substituting n = 8 in RHS, we get:
[tex]$ 5n^2 - 3n = 5(8)^2 - 3(8) = 5(64) - 24 $[/tex]
[tex]$ = 296 $[/tex]
Therefore, RHS = 296
We see, LHS = RHS
Hence, we can conclude that [tex]$ S_8 $[/tex] is correct.
