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
Solution:
Given, the 8th term of an AP is half of its 2nd term.
Also, the 11th term exceeds one third of its 4th term by 1.
We have to find the 15th term of the AP.
The nth term of the series in AP is given by
aₙ = a + (n - 1)d
When n = 8, a₈ = a + (8 - 1)d
a₈ = a + 7d
When n = 2, a₂ = a + (2 - 1)d
a₂ = a + d
Ap per given condition, a₈ = (1/2)a₂
a + 7d = (a + d)/2
2a + 14d = a + d
By grouping,
2a - a = d - 14d
a = -13d ---------------------- (1)
When n = 11, a₁₁ = a + (11 - 1) d
a₁₁ = a + 10 d
When n = 4, a₄ = a + (4 - 1)d
a₄ = a + 3d
As per given condition, a₁₁ = (1/3)a₄ + 1
a + 10d = (a + 3d)/3+ 1
3a + 30d = a + 3d + 3
By grouping,
3a - a + 30d - 3d - 3 = 0
2a + 27d - 3 = 0
2a + 27d = 3 -------------------- (2)
Substitute (1) in (2),
2(-13d) + 27d = 3
-26d + 27d = 3
d(27 - 26) = 3
d = 3
Put the value of d in (1),
a = -13(3)
a = -39
To find 15th term,
a₁₅ = -39 + (15 - 1)(3)
= -39 + (14)3
= -39 + 42
a₁₅ = 3
Therefore, the 15th term is 3.
✦ Try This: The eighth term of an AP is twice its second term and the eleventh term exceeds two third of its fourth term by 4. Find the 18th term
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 5
NCERT Exemplar Class 10 Maths Exercise 5.4 Problem 3
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
Summary:
The eighth term of an AP is half its second term and the eleventh term exceeds one third of its fourth term by 1. The 15th term is 3.
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