Question

If sum of $n$ terms of a sequence is given by $S_n=3n^2-5n+7$ and $t_r$ represents its $r^{th}$ term, then

• A. $t_7=34$
• B. $t_2=7$
• C. $t_{10}=34$
• D. $t_8=40$

Answer 1

The correct option is A $t_7=34$

$S_n=3n_2+7-5n$

$t_n=S_n-S_{n-1}$

$=(3n_2-5n+7)-\left[3\right(n-1{)}_2-5(n-1)+7]$

$=3n_2-5n+7-\left[3\right(n_2-2n+1)-5n+5+7]$

$=3n_2-5n+7-3n_2+6n-3+5n-12$

$=6n+7-3-12$

$t_n=6n+7-15$

$t_n=6n-8$

so,

$t_2=6\times 2-8=4$

$t_7=6\times 7-8=42-8=34$

$t_8=6\times 8-8=48-8=40$

$t_{10}=6\times 10-8=60-8=52$

thus,

$t_7=34$ and $t_8=40$ are correct options.