Question

what is the value of n so that n+2, 5n+1, n+11 will form a geometric sequence? find the sum the first three terms of given sequence.​

Answer 1

Answer:

First 3 terms=3,6,12 sum =21

or-7/8+2,-5*7/8+1 and -7/8+11

or 9/8, 27/8 and 81/8,sum=117/8

Step-by-step explanation:

n+2, 5n+1, n+11 are in GP

so ( 5n+1)²=(n+2)((n+11)

=25n²+10n+1=n²+13n+22

24n²-3n-21=0

8n²-n-7=0

8n²-8n+7n-7=0

8n(n-1)+7(n-7)=0

(n-1)(8n+7)=0

n=1 or -7/8

First 3 terms=3,6,12 sum =21

or-7/8+2,-5*7/8+1 and -7/8+11

or 9/8, 27/8 and 81/8,sum=117/8