in an AP sum of first n terms is 3n^2/2+13n^2/2 find its 25th term
Answers
Correct question.
If an Ap sum of first n terms is 3n²/2 + 13n/2
Find it's 25th term.
EXPLANATION.
- GIVEN
sum of n terms = 3n²/2 + 13n/2
Formula of Tn terms.
=> Tn = Sn - Sn-1
replace the value of n to n-1
=> 3n² + 13n/2
=> 3n² + 13n/2 - [ 3 ( n - 1)² + 13 ( n - 1 ) ] /2
=> 3n² + 13n/2 - [ 3 ( n² + 1 - 2n ) + 13n - 13 ]/2
=> 3n² + 13n/2 - [ 3n² + 3 - 6n + 13n - 13 ] /2
=> 3n² + 13n/2 - [ 3n² + 7n - 10 ] /2
=> 3n² + 13n - 3n² - 7n + 10 / 2
=> 6n + 10 / 2
Therefore,
Algebraic expression = 6n + 10 / 2
Let put the value of n = 1
we get,
=> 6 + 10 / 2 = 8
Let put the value of n = 2
we get,
=> 6(2) + 10 / 2 = 11
Let put the Value of n = 3
we get,
=> 6(3) + 10 / 2 = 14
Let put the value of n = 4
we get,
=> 6(4) + 10 / 2 = 17
Therefore,
Sequence = 8,11,14,17 ......
First term = a = 8
common difference = d = b - a = 3
Formula of Nth term of an Ap
=> An = a + ( n - 1 ) d
25th term of an Ap
=> a + 24d
=> 8 + 24(3)
=> 80