If the 2nd term of an AP is 13 and the 5th term is 25, what is its 7th term?
30
33
37
38
Step 1: Recall the formula for the nth term of an AP: \(a_n = a + (n-1) d\), where \(a\) is the first term, and \(d\) is the common difference.
Step 2: The 2nd term is given as 13. Using the formula: \(a_2 = a + (2-1)d = a + d\). So, \(a + d = 13\). (Equation 1)
Step 3: The 5th term is given as 25. Using the formula: \(a_5 = a + (5-1)d = a + 4d\). So, \(a + 4d = 25\). (Equation 2)
Step 4: Subtract Equation (1) from Equation (2): \((a + 4d) - (a + d) = 25 - 13\) \(3d = 12\) \(d = 4\).
Step 5: Put the value of \(d\) into Equation (1): \(a + 4 = 13\) \(a = 9\).
Step 6: Now find the 7th term: \(a_7 = a + (7-1)d = 9 + 6 \times 4 = 9 + 24 = 33\).
Final Answer: The 7th term is 33.