Question

how many terms in the series 1,4,7,10.... amount to 176​

Answer 1

Solution:-

Given A.P. :-

1 , 4 , 7 , 10 , ........

• First Term ( a ) = 1
• Common Difference ( d ) = 4 - 1 = 3
• Sum of nth term ( Sn ) = 176

To Find:-

n = ?

Find:-

Sn = n/2 [ 2a + ( n - 1 )d ]

=) 176 = n/2 [ 2 + ( n - 1 )3 ]

=) 176 × 2 = n [ 2 + 3n - 3 ]

=) 352 = n [ 3n - 1 ]

=) 352 = 3n² - n

=) 3n² - n - 352 = 0

=) 3n² - ( 33 - 32 )n - 352 = 0

=) 3n² - 33n + 32n - 352 = 0

=) 3n ( n - 11 ) + 32 ( n - 11 ) = 0

=) ( n - 11) and ( 3n + 32 )

=) [ n = 11 ] and [ n = 32/3 = 10.6 ]

[ n = 10.6 ] Neglected as the Number of term can't be in Decimal.

=) n = 11.