Question

How many terms of the A.P. 7, 11, 15, 19, 23, ............ must be taken to get the sum 250 ?????

Answer 1

HELLO DEAR,



GIVEN THAT :-

a=7. and d=11-7=4


now, let the the term taken be (n)

given that:-sn =250

$s_{n } = \frac{n}{2} (2a + (n - 1)d) = 250 \\ = > 500 = n(2 \times 7 + (n - 1) \times 4 \\ = > 500 = n(14 - 4 + 4n) \\ = > 500 = 10n + 4 {n}^{2} \\ = > 4 {n}^{2} + 10n - 500 = 0 \: \: \: \: (divide \: \: both \: side \: by \: (2)\\ = > 2 {n}^{2} + 5n - 250 = 0 \\ = > 2 {n}^{2} + 25n - 20n - 250 = 0 \\ = > 2n(n + 25) - 20(n + 25) \\ = > (2n - 20)(n + 25) \\ = > n = \frac{20}{2} = 10 \\ = > n = - 25$

Answer 2

.....................................