Question 1142569
{{{ x[n] = a + d*( n-1 ) }}}
{{{ d }}} = the difference between successive terms
{{{ n }}} = the number of the term
{{{ a }}} = the first term
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{{{ 1/2 = a + d*( 7 - 1 ) }}}
(1) {{{ 1/2 = a + 6d }}}
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{{{ 6 = a + d*( 14 - 1 ) }}}
(2) {{{ 6 = a + 13d }}}
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subtract (1) from (2)
(2) {{{ 6 = a + 13d }}}
(1) {{{ -1/2 = -a - 6d }}}
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{{{ 11/2 = 7d }}}
{{{ d = 11/14 }}}
and
(2) {{{ 6 = a + 13*(11/14) }}}
(2) {{{ a = 84/14 - 143/14 }}}
(2) {{{ a = -59/14 }}}
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{{{ x[10] = -59/14 + ( 11/14 )*( 10 - 1 ) }}}
{{{ x[10] = -59/14 + 99/14 }}}
{{{ x[10] = 40/14 }}}
{{{ x[10] = 20/7 }}}
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check answer:
What is the 7th term?
{{{ x[7] = -59/14 + ( 11/14 )*( 7 - 1 ) }}}
{{{ x[7] = -59/14 + 66/14 }}}
{{{ x[7] = 7/14 }}}
{{{ x[7] = 1/2 }}}
What is the 14th term?
{{{ x[14] = -59/14 + ( 11/14 )*( 14 - 1 ) }}}
{{{ x[14] = -59/14 + 143/14 }}}
{{{ x[14] = 84/14 }}}
{{{ x[14] = 6 }}}
OK