translate into math:
The fifth term of an eponential sequence is 4375 ----> ar^4 = 4375
the second term is 35 ----> ar = 35
divide the first equation by the second:
ar^4/(ar) = 4375/35
r^3 = 125
r = 5 <----- the cube root of r^3 is r, the cube root of 125 is 5
now sub that into ar=35 to find a
the rest is routine by simply using your formulas for "sixth term" and the "sum of first five terms?
The fifth term of an eponential sequence is 4375 and the second term is 35. Find the third , sixth term and sum of the of the first five term
2 answers
an = a1 ∙ r ⁿ⁻¹
a2 = a1 ∙ r ²⁻¹
a2 = a1 ∙ r¹
a2 = a1 ∙ r = 35
a5 = a1 ∙ r ⁵⁻¹
a5 = a1 ∙ r⁴
4375 = a1 ∙ r ∙ r³
4375 = 35 ∙ r³
r³ = 4375 / 35 = 125
r = ∛125
r = 5
a1 ∙ r = 35
a1 ∙ 5 = 35
a1 = 35 / 5 = 7
a1 = 7
Now use formula:
an = a1 ∙ r ⁿ⁻¹
to find other terms
and formula for nth partial sum of a geometric sequence:
Sn = a1 ( 1 - rⁿ ) / ( 1 - r )
S5 = a1 ∙ ( 1 - 5⁵ ) / ( 1 - 5 )
S5 = 7 ∙ ( 1 - 3125 ) / - 4
S5 = 7 ∙ ( - 3124 ) / - 4
S5 = 5467
a2 = a1 ∙ r ²⁻¹
a2 = a1 ∙ r¹
a2 = a1 ∙ r = 35
a5 = a1 ∙ r ⁵⁻¹
a5 = a1 ∙ r⁴
4375 = a1 ∙ r ∙ r³
4375 = 35 ∙ r³
r³ = 4375 / 35 = 125
r = ∛125
r = 5
a1 ∙ r = 35
a1 ∙ 5 = 35
a1 = 35 / 5 = 7
a1 = 7
Now use formula:
an = a1 ∙ r ⁿ⁻¹
to find other terms
and formula for nth partial sum of a geometric sequence:
Sn = a1 ( 1 - rⁿ ) / ( 1 - r )
S5 = a1 ∙ ( 1 - 5⁵ ) / ( 1 - 5 )
S5 = 7 ∙ ( 1 - 3125 ) / - 4
S5 = 7 ∙ ( - 3124 ) / - 4
S5 = 5467
2 answers