Question

1.the eighth term of an AP is half its second term and the eleventh term exceeds one third of its fourth term by 1.Find the 15th term.

2.find the sum of the integers betweem 1000 and 2000 that are

(i)divisible by 9 (ii) not divisible by 9

[hint (ii); these numbers will be ; total numbers - total numbers divisible by 9.]

Answer 1

this is 1 part and 2 part's 1 portion
second portion is
the sum of no. not divisible by 9 = total sum of digits - sum of no. divisible by 9
total sum = 1498500
sum of no. divisible by 9 = 166833
hence, sum of no. divisible by 9 = 1498500-166833 = 1331667
sorry space was over in page so I was no able to show you the pic

Answer 2

We need to find in this question is a 15th term of an ap. So let start   Sol.....             A8=a+7d=a+d/2                 2(a+7d)=a+d             2a+14d= a+d         2a-a+14d-d=0     a+13d=0.       ...... (i)   A+10d=a+3d/3+1      A+10d=(a+3d+3)/3             3(a+10d)=a+3d+3                   3a-a+30d-3d-3=0                          2a+27d=3.          ... (ii)  Solve (i)&(ii)  Eq(i) multiply by 2       2a+26d=0......(iii)       2a+27d=3.......(iv) Solve (iii) & (iv)  D=3 Put d in (i)  A+39=0  A= -39****   D=3**** A15=a+14d       =.  - 39+14(3)=.  - 39+42=. 3 A15 is 3***             Answer is 3....        I hope this answer helps u