Finding the $n$th term of an AP

Correct answer: B. 14

The first term is \(a=14\) and the common difference is \(d=14-14=0\). Hence, \(a_n=a+(n-1)d=14+(n-1)\times 0=14\). Therefore, the 40th term is 14. The value 560 is \(14\times 40\), but an AP term is not found by multiplying the first term by its position. Exam tip: if all terms of an AP are equal, its common difference is 0 and every term equals the first term.

Correct answer: B. (\frac{29}{5})

Here (d=1), so (a_6=\frac{4}{5}+5=\frac{29}{5}). Convert the whole number to a fraction with the same denominator.

Correct answer: B. 211

The sequence is given directly by the nth-term rule a_n=6n+7. To find the 34th term, substitute n=34: a_34=6(34)+7=204+7=211. Therefore option B is correct. The nearby alternatives result from arithmetic or substitution errors; for example, 6(34)=204, not 200 or 208, and the final addition must include the constant 7.