Question

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

NCERT Class X
Mathematics - Exemplar Problems

Chapter _ARITHMETIC PROGRESSIONS

Answer 1

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

Answer 2

Answer:

Step-by-step explanation:

a + 7d = a + d/2

=>2a + 14d = a + d

a = -13d

a + 10d = 1/3(a + 3d) + 1

a + 10d -1 = 1/3(a + 3d)

3(a + 10d -1) = a +3d

3a + 30d -3 = a + 3d

2a + 27d =3

2(-13d) + 27d =3(since a = -13d)

-26d + 27d = 3

=> d = 3

a= -13d

=> a = -39

a + 14d = -39 + 42

hence a15 =3