Question

please help me please​

Answer 1

Step-by-step explanation:

$Given:\: a = - 5, \:t_n = 45,\: S_n=120 \\ \\ \because \: S_n = \frac{n}{2} (a + t_n) \\ \\ \therefore \: 120 = \frac{n}{2} ( - 5 + 45) \\ \\ \therefore \: 120 = \frac{n}{2} \times 40 \\ \\ \therefore \: 120 = n \times 20 \\ \\ \therefore \: 20 \: n = 120 \\ \\ \therefore \: n = \frac{120}{20} \\ \\ \huge \purple{ \boxed{\therefore \: n = 6}} \\ \\ \because \: t_n = a + (n - 1)d \\ \\ \therefore \: 45 = - 5 + (6 - 1) \times d \\ \\ \therefore \: 45 + 5 = 5 d \\ \\ \therefore \: 50 = 5 d \\ \\ \therefore \:d = \frac{50}{5} \\ \\ \huge \orange{ \boxed{ \therefore \:d = 10}}$

Hence,

Number of terms = 6

Common Difference = 10