Question

How many terms must be taken of the series: -5,-1,3... to make the sum 897?

Answer 1

Step-by-step explanation:

a=-5,d=-1-(-5)=-1+5=4 Sn= 897

$sn = \frac{n}{2} (2a + (n - 1)d \\ 897 \times 2 = n(2( - 5) + (n - 1)(4) \\ 1794 = n( - 10 + 4n - 4) \\ 1794 = n(4n - 14) \\ 4 {n}^{2} - 14n - 1794 = 0 \\ 4 {n}^{2} - 92n + 78n- 1794 = 0 \\ 4n(n - 23) + 78(n \: - 23) = 0 \\ (n - 23)(4n + 78) = 0 \\ n - 23 = 0 \: \: \: \: or \: \: 4n + 78 = 0 \\ n = 23 \: \: \: or \: n = - \frac{78}{4} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: n > 1 \\ so \: n = 23$

in series have 23 terms them sums are 897