Question

A geometric progression has 6 term if the 3 and 4 term are 28 and-56 resptively find the first term

Answer 1

a3 = 28

a4 = 56

In GP common ratio:

r = an / a(n-1)

In this case;

r = a4 / a3 = 56 / 28

r = 2

The n-th term of GP:

an = a1ⁿ ⁻ ¹

a3 = a1 ∙ r²

28 = a1 ∙ 2² = a1 ∙ 4

4 a1 = 28

a1 = 28 / 4

a1 = 7

OR

a4 = a1 ∙ r³

56 = a1 ∙ 2³ = a1 ∙ 8

8 a1 = 56

a1 = 56 / 8

a1 = 7

Your GP is:

7 , 14 , 28 , 56 , 112 , 224

Since your GP has 6 terms maybe you need to find the sum of the first six terms.

The sum of the first n members in GP:

Sn = a1 ( rⁿ - 1 ) / ( r - 1 )

In this case n = 6 , a1 = 7 , r = 2.

S6 = 7 ∙ ( 2⁶ - 1 ) / ( 2 - 1 ) = 7 ∙ ( 64 - 1 ) / 1 = 7 ∙ 63

S6 = 441

You check that:

7 + 14 + 28 + 56 +112 + 224 = 441

Answer 2

r = -2