Question

In an ap,the sum of first n term is 3n2/2+13n/2. find its 25th term

Answer 1

n term sum = 3n²/2 + 13n/2

as we know that nth term = (Sum of nth term ) -( sum of (n-1)th term)

method 1

so 25th term = (sum of 25 terms) - ( sum of 24 terms)

                     =(3×(25)²/2 +(13×25)/2) - ( 3×(24)²/2 + (13×24)/2)

                     = 1100 - 1020

                     = 80

method 2

1st term = 8

sum of 2 terms = 19

2nd term = 19 - 8= 11

so. difference = 11- 8 = 3

25th term = (8 + (25 -1)×3) = 80

Answer 2

put n in this type question we get s1, s2 so on

so n=1 and n=1 is also A( first term)

by put n=1

s1= 3(1)2/2+13(1)/2

= 3/2+13/2

= (3+13)/2 by lcm

=16/2

= 8

sum of first term is 8 and first term is also 8

we need second term to find common difference

put n=2 ( but n =2 is not second term)

s2= 3(2)2/2+13(2)/2

= 3(4)/2+26/2

= 12/2+26/2

= (12+26) /2 by lcm

= 38/2

= 19 ( is sum of second term not a second term)

for second term

we do

s2-s1= second term

19-8=11

so a2=11

a25=(8+(25-1)3 ) ( d = a2-a1 =11-8=3)

by using this formula an= (a+(n-1)×d)

a25= 8+24×3

= 8 +72

= 80

25 term is 80

I hop it help u thank

but please select my answer as the brainliest