Common Difference = 3
Explanation:
Given:
First term of AP is 7.
Last term of AP is 49.
Sum of all terms of AP is 420.
To Find:
What is the common difference of the AP ?
Solution: Let the common difference and number of terms of AP be d and n respectively.
a = first term = 7
d = common difference
l = last term = 49
Sⁿ = sum of all terms = 420
As we know that , Sum of n term of an AP is
★Sⁿ = n/2 × ( a + l )
⟹ 420 = n/2 ( 7 + 49 )
⟹ 420 × 2 = 56n
⟹ 840/56 = n
⟹ 15 = n
So the given AP series contains 15 terms and last term of AP will be given by -
➙ a + (n – 1)d = 49
➙ 7 + (15 – 1)d = 49
➙ 14d = 49 – 7
➙ d = 42/14
➙ d = 3
Hence, the common difference of AP series is 3.