Question

If the sum to first n terms of an A.P. is (3n2/2 + 5n/2), find its 25th term.
(Ans =76) pls show the procedure step by step ​

Answer 1

Answer:

n/2(2a+(n-1)d)=sum of terms

n/2(2a+(n-1)d)=3n2/2+5n/2

1/2(2a+(n-1)d=3n/2+5/2

a+(n-1)d/2=3n/2+5/2

for 25th term

n=49

a+24d=152/2

a+24d=76

therefore 25th term is 76

hence proved

Answer 2

Important variables In the following explanation :- a- first term d-common difference

Step-by-step explanation:

$\frac{3 {n}^{2} }{2} + \frac{5n }{2} = \frac{n}{2} (5 + 3n)$

$\frac{n}{2} (5 + 3n) = \frac{n}{2} (2 \times 4 + (n - 1)3)$

-——--------------------(1)

we know that sum of n terms of an A.P is

$\frac{n}{2} (2a + (n - 1)d)$

comparing (1) and this equation

we get a =4

d = 3

we know that nth term of an A.P is a+(n-1)d

so 25th term is 4+(25-1)3

=4+72=76

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