Question

10 term of an AP is 21 and sum of first 10th term is 120 find 25th term of the AP​

Answer 1

Answer:

Given,10th term of the AP is (a10)=21

sum of the first 10th term is (S10)=120

Let, the 25th term of the AP is a25

Now, a10=21

=>a+(10-1)d=21

=>a+9d=21

=>a=21-9d••••••••••••(i)

Again,S20=120

=>n/2{2a+(n-1)d}=120

=>20/2{2(21-9d)+(20-1)d}=120

=>10{(42-18d+19d)}=120

=>42+d=12

=>d= 12-42

=>d= -30

Now, putting the value of d in eq.n (i) we get,

a=21-9(-30)

=21+270

=291

Hence, the 25th term of the AP will be,

a+(n-1)d=291+(25-1)(-30)

=291+(24)(-30)

=292-720

= -428