Which term of the AP: 3, 8, 13, 18, . . . , is 78?

Question 8 of 44beginner🔧 ApplyShort Answer2 marks

Correct Answer

16th term

Exercise: EXERCISE 5.2 | Q: 4 | (Page Page 14)

For More Understanding

Explanation

This problem is solved using the nth term formula of an Arithmetic Progression, $a_n = a + (n - 1)d$ . Similar to Example 6 provided in the context, we treat the known value (78) as the nth term and solve the linear equation for 'n'. Since the resulting value of n is a positive integer, the term exists in the AP.

Solution Steps

Step 1: Identify the first term ( $a$ ) and common difference ( $d$ ) from the AP: 3, 8, 13, 18, . . . Here, a = 3 and d = 8 - 3 = 5.
Step 2: Let the term 78 be the $n$ th term ( $a_n$ ). Use the formula: $a_n = a + (n - 1)d$ .
Step 3: Substitute the values into the formula: $78 = 3 + (n - 1)5$ .
Step 4: Solve for $n$ : $78 - 3 = 5(n - 1) \Rightarrow 75 = 5(n - 1) \Rightarrow 15 = n - 1 \Rightarrow n = 16$ .

Previous Next