If 4 5 , a , 2 are in A P , find the value of a .

If 4 5 , a and 2 are three consecutive terms of an A P , then we have: a - 4 5 = 2 - a ( ∵ Common difference) ⇒ 2 a = 2 + 4 5 ⇒ 2 a = 14 5 ⇒ a = 7 5

If 4 5 , a , 2 are in A P , find the value of a .

If 4 5 , a and 2 are three consecutive terms of an A P , then we have: a - 4 5 = 2 - a ( ∵ Common difference) ⇒ 2 a = 2 + 4 5 ⇒ 2 a = 14 5 ⇒ a = 7 5

If 1 + 4 + 7 + 10 + … + x = 287 , find the value of x .

Given that, 1 + 4 + 7 + 10 + … + x = 287 Here, a = 1 , d = 4 - 1 = 3 and s n = 287 287 = n 2 [ 2 + ( n - 1 ) 3 ] ⇒ 574 = n ( 2 + 3 n - 3 ) ⇒ 3 n 2 - n - 574 = 0 Using the quadratic formula x = - b ± b 2 - 4 a c 2 a , n = - ( - 1 ) ± ( - 1 ) 2 - 4 ( 3 ) ( - 574 ) 2 ( 3 ) ⇒ n = 1 ± 1 + 6888 6 ⇒ n = 14 , - 41 3 Number of terms can not be negative So, n = 14 Now, S n = n 2 [ a + l ] ⇒ 287 = 14 2 [ 1 + x ] ⇒ x = 40