Question

the 8th term of an ap is half of its second term and 11th term exceeds one third of its fourth term by 1. find the 15th term...



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Answer 1

Answer:

3

Step-by-step explanation:

Given, an A.P in which,

a8 = 1/2(a2) a11 = 1/3(a4) + 1

We know that an = a + (n – 1)d

⇒ a8 = 1/2(a2) a + 7d = 1/2(a + d) 2a + 14d = a + d a + 13d = 0 …… (i)

And, a11 = 1/3(a4) + 1 a + 10d = 1/3(a + 3d) + 1 3a + 30d = a + 3d + 3 2a + 27d = 3 …… (ii)

Solving (i) and (ii), by (ii) – 2x(i)

⇒ 2a + 27d – 2(a + 13d) = 3 – 0 d = 3

Putting d in (i) we get, a + 13(3) = 0 a = -39

Thus, the 15th term a15 = -39 + 14(3) = -39 + 42 = 3

Answer 2

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