Question 1086266
The formula is:
{{{ a[n] = a[1] + ( n-1 )*d }}}
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You are given that:
{{{ a[4] = 5 }}}
{{{ a[14] = 10 }}}
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(1) {{{ a[4] = a[1] + ( 4-1 )*d }}}
(1) {{{ 5 = a[1] + 3d }}}
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(2) {{{ a[14] = a[1] + ( 14 - 1 )*d }}}
(2) {{{ 10 = a[1] + 13d }}}
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Subtract (1) from (2)
(2) {{{ 10 = a[1] + 13d }}}
(1) {{{ -5 =- a[1] - 3d }}}
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{{{ 5 = 10d }}}
{{{ d = 1/2 }}}
and
(1) {{{ 5 = a[1] + 3d }}}
(1) {{{ 5 = a[1] + 3*(1/2) }}}
(1) {{{ a[1] = 5 - 3/2 }}}
(1) {{{ a[1] = 7/2 }}}
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a)
{{{ a[n] = 7/2 + ( n-1 )*(1/2) }}}
relates number of miles, {{{ a[n] }}} and week number {{{ n }}}
b)
{{{ a[n] = 26 }}}
{{{ a[n] = 7/2 + ( n-1 )*(1/2) }}}
{{{ 26 = 7/2 + ( n-1 )*(1/2) }}}
{{{ 52 = 7 + n - 1 }}}
{{{ n = 46 }}}
In week 46 she would run at least 26 mi
c)
The assumption is that the sequence would continue
to be arithmetic no matter how big {{{ n }}} is