Question

The first term and the last term of an A.P. are 8 and 341 respectively. If the common difference is 9, then find the number of terms in it and their sum.

Hint:

When the last term is known, the $S_n = \frac{n}{2}(a+l)$ formula is much faster than the $S_n = \frac{n}{2}[2a+(n-1)d]$ formula.

Answer 1

Step 1: Understanding the Concept:
We use the $n^{th}$ term formula $a_n = a + (n-1)d$ to find the number of terms ($n$), and the sum formula $S_n = \frac{n}{2}(a + a_n)$ for the total.
Step 2: Finding n:
Given: $a = 8, a_n = 341, d = 9$. \[ 341 = 8 + (n-1)9 \] \[ 333 = (n-1)9 \] \[ n-1 = 37 \implies n = 38 \]
Step 3: Finding the Sum:
\[ S_{38} = \frac{38}{2}(8 + 341) \] \[ S_{38} = 19 \times 349 = 6631 \]
Step 4: Final Answer:
The number of terms is 38 and their sum is 6631.