Question

If -2/7,m,-7/2(m+2)........... are in GP find the value of m

Answer 1

Answer:

m = 2 , m = -1

we will accept -1 because its a sequence of negative numbers

Step-by-step explanation:

A geometric sequence is a sequence such that any element after the first is obtained by multiplying the preceding element by a constant called the common ratio which is denoted by r

a(n) = a1r^(n-1)

where r common ratio

             a1 first term

            an-1 the term before the n th term

            n          number of term

Equation1

a2 = a1 r ^(2-1)

m = 2/7 r  ^1

m = 2/7r

r = 7m/2

Equation2

a3= a1 r ^( 3-1 )

-7/2(m+2) = -2/7 (7m/2)^2

-7m/2 -14/2 = -2/7   (49m²/4)

-7m/2 -14/2 = -98m²/28

98m²/28 - 7m/2  -14/2 = 0

solving the quadratic equation

m = 2 , m = -1