An arithmetic sequence has a first term of 5 and a common difference of 3. Find the 10th term of the sequence.
Question Q1
An arithmetic sequence has a first term of 5 and a common difference of 3. Find the 10th term of the sequence.
Mark Scheme
Step 1: Identify given information.
$u_1 = 5$, $d = 3$, $n = 10$.
Step 2: Use formula $u_n = u_1 + (n-1)d$.
$u_{10} = 5 + (10-1)3$
Step 3: Calculate.
$u_{10} = 5 + (9)3 = 5 + 27 = 32$.
Answer: 32
For the sequence in Q1a, find the sum of the first 20 terms.
Question Q2
For the sequence in Q1a, find the sum of the first 20 terms.
Mark Scheme
Step 1: Identify given information.
$u_1 = 5$, $d = 3$, $n = 20$.
Step 2: Use formula $S_n = frac{n}{2}(2u_1 + (n-1)d)$.
$S_{20} = frac{20}{2}(2(5) + (20-1)3)$
Step 3: Calculate.
$S_{20} = 10(10 + (19)3) = 10(10 + 57) = 10(67) = 670$.
Answer: 670
