Correct Answer - Option 1 : 17
Concept:
The nth number in A.P. series = Tn = a + (n - 1)d
Where 'a' is the first number of the series and 'd' is the common difference
Calculation:
Let the first element of A.P. is 'a' and the common difference is 'd'
Given:
2nd and 5th terms in the arithmetic progression are 7 and 13 respectively.
The second term = 7
⇒ a + d = 7 ----(i)
And the fifth term = 13
⇒ a + 4d = 13 ----(ii)
After subtracting equation (ii) from equation(i) we get,
⇒ 4d - d = 13 - 7
⇒ 3d = 6
⇒ d = 2
Put the value of d in equation (1), we get
⇒ a + 2 = 7
⇒ a = 7 - 2
⇒ a = 5
Now 7th term = a + 6d
= 5 + 6 × 2
= 5 + 12
= 17
∴ The 7th term in arithmetic series is 17
