The 4th term from the end of the AP: \(-11,-8,-5,\ldots,49\) is
37
40
43
58
Step 1: Identify the first term and common difference.
The first term \(a = -11\).
The numbers are increasing by 3 each time, so the common difference \(d = 3\).
Step 2: Find how many terms are there in the AP.
The last term is given as \(l = 49\).
The formula to find the number of terms in an AP is:
\(n = \dfrac{l - a}{d} + 1\).
Substitute the values: \(n = \dfrac{49 - (-11)}{3} + 1 = \dfrac{60}{3} + 1 = 20 + 1 = 21\).
So, there are 21 terms in this AP.
Step 3: Understand what "4th term from the end" means.
If there are 21 terms in total, the last term is the 21st term. The 4th from the end means:
21st → last term
20th → 2nd from the end
19th → 3rd from the end
18th → 4th from the end
So we need to find the 18th term.
Step 4: Find the 18th term.
The formula for the \(n\)th term is: \(a_n = a + (n-1)d\).
Put \(n = 18\):
\(a_{18} = -11 + (18 - 1) \times 3\).
\(a_{18} = -11 + 17 \times 3\).
\(a_{18} = -11 + 51 = 40\).
Final Answer: The 4th term from the end is 40.