NCERT Class 11-Math's: Chapter –9 Sequence and Series Part 4

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Question 10:

If are in A.P. with common difference ; then the sum of the series is equal to

Answer:

We have

Question 11:

(i) If are four distinct positive quantities in A.P., then show that

(ii) If are four distinct positive quantities in G.P., then show that

Answer:

(i) Since are in A.P., then A., for the first three terms.

Therefore,

Squaring, we get

Similarly, for the last three terms

Multiplying (1) and (2), we get

(ii) Since are in G.P.

Again . for the first three terms

Similarly, for the last three terms

b + d > 2c ... (4)

Adding (3) and (4), we get

Question 12:

If are three consecutive terms of an A.P. and are three consecutive terms of a G.P. Then prove that

Answer:

We have as three consecutive terms of A.P. Then

Now

Question 13:

Find the natural number a for which where the function satisfies or all natural numbers and further .

Answer:

Given that

Therefore,

And so on. Continuing the process, we obtain

But, we are given

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