Multiple choice

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

  1. $t_{7} = 34$
  2. $t_{2} = 7$
  3. $t_{10} = 34$
  4. $t_{8} = 40$
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A Correct answer
AI explanation

To find a specific term when the sum is known, use the formula t_r = S_r - S_(r-1). For the 7th term, calculate S_7 = 3(49) - 5(7) + 7 = 147 - 35 + 7 = 119. Then calculate S_6 = 3(36) - 5(6) + 7 = 108 - 30 + 7 = 85. Therefore, t_7 = 119 - 85 = 34.