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