Share

# In an A.P., the Sum of First N Terms is (3n^2)/2 + 13/2 N. Find Its 25th Term. - CBSE Class 10 - Mathematics

ConceptSum of First n Terms of an AP

#### Question

In an A.P., the sum of first n terms is (3n^2)/2 + 13/2 n. Find its 25th term.

#### Solution

Here, the sum of first n terms is given by the expression,

S_n = (3n^2)/2 + 13/2 n

We need to find the 25th term of the A.P.

So we know that the nthterm of an A.P. is given by,

a_n = S_n- S_(n - 1)

So a_25 = S_25 - S_24 ....(1)

So, using the expression given for the sum of n terms, we find the sum of 25 terms (S25) and the sum of 24 terms (S24). We get,

S_25 = (3(25)^2)/2 + 13/2 (25)

= (3(25)^2)/2 + 13/2 (25)

= (3(625))/2 + (13(25))/2

= 1875/2 = 325/2

= 2200/2

= 1100

Similarly

S_24 = (3(24)^2)/2 + 13/2 (24)

= (3(576))/2 + (13(24))/2

= 1728/2 + 312/2

= 2040/2

=1020

Now, using the above values in (1),

a_25 = S_25 - S_24

= 1100 - 1020

= 80

Therefore a_25 = 80

Is there an error in this question or solution?

#### Video TutorialsVIEW ALL [5]

Solution In an A.P., the Sum of First N Terms is (3n^2)/2 + 13/2 N. Find Its 25th Term. Concept: Sum of First n Terms of an AP.
S