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.
Answers
Answer:
The common Difference is 3.
Step-by-step explanation:
Given :
first term, a = 2, last term, l = 50, Sn = 442
By using the formula ,Sum of nth terms , Sn = n/2 [a + l]
442 = n/2 [50 + 2]
442 = n/2 × 52
442 = 23n
n = 442/23
n = 17
By using the formula, l = a + (n - 1)d
50 = 2 + (17 - 1)d
50 - 2 = 16d
48 = 16d
d = 48/16
d = 3
Common Difference ,d = 3
Hence, the common Difference is 3.
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GIVEN :
First Term of an AP = a = 2
Last Term = an = 50
Sum of these terms = 442
Difference = ?
In an AP an = a + ( n - 1 )d
50 = a + (n - 1)d
50 = 2 + (n - 1)d
48 = dn - d ------(1)
In an AP sum of the terms = n/2 ( a + an )
= n/2 ( 2a + eq - 1 )
Substitute equation - 1 in the above formula.
442 = n/2 ( 2a + dn - d )
442 = n/2 ( 2(2) + 48 )
442 = n/2 ( 4 + 48 )
442 = n/2( 52 )
442 = 26n
n = 442/26
n = 17
Thus, n = 17.
Substitute this in eq - 1
48 = dn - d
48 = d(17) - d
48 = 17d - d
48 = d(17 - 1)
48 = d (16)
d = 48/16
d = 3
Therefore, common difference between the terms is 3.