1.

the product of 30th,40th, and 50th terms of a GS is 512. If the 20th terms of an AS is equal to the 40th term of the GS,find the sum of first 39 terms of the AS.

Answer»

Step-by-step EXPLANATION:

Let the 3 number in the geometric sequence be a/R, a and ar.

The PRODUCT of the three numbers is a^3 = 512, So a = 8.

Now (a/r) +8, a+6, ar form an AP.

So we have: ar - (a+6) = a+6 - (a/r)-8, or

ar^2-ar-6r = ar+6r-a-8r, or

8r^2–8r-6r = 8r+6r-8–8r, or

8r^2–14r-6r +8 = 0

8r^2–20r+8 = 0, or

2r^2–5r +2= 0, or

(2r-1)(r-2) = 0

Hence r =2 or 1/2.

So the three terms of the GP are 4, 8 and 16 or 16, 8 and 4.

Check: 4+8, 8+6, 16 = 12, 14 16, all in AP. Correct.

16+8, 8+6, 4 = 24, 14, 4, all in AP. Correct.

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