In an A.P, the first term is 2 and the sum of the first five terms is one-fourth of the next five terms.

Question

In an A.P, the first term is 2 and the sum of the first five terms is one-fourth of the next five terms. Show that 20^th term is –112.

Asked by Pragya Singh | 1 year ago | 98

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Class 11 Maths Sequences and Series Add Answer

Class 11 Maths Sequences and Series View Answer

Class 11 Maths Sequences and Series View Answer

If a is the G.M. of 2 and \( \dfrac{1}{4}\) find a.

Class 11 Maths Sequences and Series View Answer

Find the geometric means of the following pairs of numbers:

(i) 2 and 8

(ii) a³b and ab³

(iii) –8 and –2

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Insert 5 geometric means between \( \dfrac{32}{9}\) and \( \dfrac{81}{2}\).

Class 11 Maths Sequences and Series View Answer

Accepted Answer

The first term (a) of an A.P = 2

Let’s assume d be the common difference of the A.P.

So, the A.P. will be 2, 2 + d, 2 + 2d, 2 + 3d, …

Then,

Sum of first five terms = 10 + 10d

Sum of next five terms = 10 + 35d

From the question, we have

10 + 10d = \( \dfrac{1}{4}\)(10 + 35d)

40 + 40d = 10 + 35d

30 = -5d

d = -6

a₂₀ = a + (20 – 1)d = 2 + (19) (-6) = 2 – 114 = -112

Therefore, the 20^th term of the A.P. is –112.

Answered by Abhisek | 1 year ago