Question

If 1st and 4tg terms of G.p are 500 and 32 respectively it's second term is ?

Answer 1

`T_(2) = 200`

Explanation:

Given

Geometry Progression

`T_1 = 500`

`T_4 = 32`

Required

Calculate the second term

First, we need to write out the formula to calculate the nth term of a GP

`T_n = ar^(n-1)`

For first term: Tn = 500 and n = 1

`500 = ar^(1-1)`

`500 = ar^(0)`

`500 = a`

`a = 500`

For fought term: Tn = 32 and n = 4

`32 = ar^(4-1)`

`32 = ar^3`

Substitute 500 for a

`32 = 500 * r^3`

Make r^3 the subject

`r^3 = (32)/(500)`

`r^3 = 0.064`

Take cube roots

`\sqrt[3]{r^3} = \sqrt[3]{0.064}`

`r = \sqrt[3]{0.064}`

`r = 0.4`

Using:
`T_n = ar^(n-1)`

`n = 2`
`r = 0.4` and
`a = 500`

`T_(2) = 500 * 0.4^(2-1)`

`T_(2) = 500 * 0.4^1`

`T_(2) = 500 * 0.4`

`T_(2) = 200`

Hence, the second term is 200