Determine the AP whose third term is 16 and the 7th term exceeds the 5th term by 12
Solution:
aₙ = a + (n - 1)d is the nth term of an AP, where aₙ is the nth term, a is the first term, d is a common difference and n is the number of terms.
Let a be the first term and d the common difference.
According to the question, a₃ = 16 and a₇ - a₅ = 12
a + (3 - 1)d = 16
a + 2d = 16 ... equation(1)
Using a₇ - a₅ = 12
[a + (7 - 1) d] - [a + (5 - 1) d] = 12
[a + 6d] - [a + 4d] = 12
2d = 12
d = 6
By substituting this in equation (1), we obtain
a + 2 × 6 = 16
a + 12 = 16
a = 4
Therefore, A.P. will be 4, 4 + 6, 4 + 2 × 6, 4 + 3 × 6, ...
Hence, the sequence will be 4, 10, 16, 22, ...
☛ Check: NCERT Solutions for Class 10 Maths Chapter 5
Video Solution:
Determine the A.P. whose third term is 16 and the 7th term exceeds the 5th term by 12
NCERT Solutions Class 10 Maths Chapter 5 Exercise 5.2 Question 16
Summary:
The AP whose third term is 16 and the 7th term exceeds the 5th term by 12 is 4, 10, 16, 22,…
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