If the 12th term of an ap is 213 and sum of its first four terms is 24 then what is the sum of its first 10terms?
Answers
Given : 12th term of an AP is 213 and the sum of its four term is 24
To Find : what is the sum of its first 10 terms
Solution:
aₙ = a + (n-1)d
Sₙ = (n/2)(2a + (n-1)d)
12th term of an AP is 213
=> a + 11d = 213
sum of its four term is 24
(4/2)(2a + 3d) = 24
=> 2a + 3d = 12
a + 11d = 213 => 2a + 22d = 426
2a + 3d = 12
=> 19d = 414
=> d = 414/19
a + 11d = 213
=> a = 213 - 11d
=> a = 213 - 11 * 414/19
=> a = -507/19
Sum of 10th terms = (10/2)(2a + 9d)
= 5(2( -507/19) + 9(414/19))
=(5/19)2712
= 13560/19
=713.684
sum of its first 10 terms = 13560/19 =713.684
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