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Question
The first term of an A.P. is 2 and the last term is 50. The sum of all these terms is 442. Find the common difference.
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Solution
Let the number of terms of the given A.P. be n, first term be a and the common difference be d.
First term a = 2
Last term l = 50
Sum of all the terms Sn = 442
We know that,
Sum of the n terms Sn = `n/2(a + l)`
`=> 442 = n/2 (2 + 50)`
`=> 442 = n(26)`
`=> n = 442/26`
⇒ n = 17
Also,
l = a + (n - 1)d
Therefore,
On substituting the values of a, l and n, we get,
50 = 2 + (17 - 1)d
⇒ 50 = 2 + 16d
⇒ 50 - 2 = 16d
⇒ 48 = 16d
⇒ `48/16` = d
⇒ d = 3
Hence, the common difference of the given A.P. is 3.
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