Suppose a 1 , a 2 , 2 , a 3 , a 4 be in an arithmetico-geometric progression. If the common ratio of the corresponding geometric progression is 2 and the sum of all 5 terms of the arithmetico-geometric progression is 49 2 , then a 4 is equal to ______________

Step-by-step solution

Given, a 1 , a 2 , 2 , a 3 , a 4 be in an arithmetico-geometric progression, And the common ratio of the corresponding geometric progression is 2 and the sum of all 5 terms of the arithmetico-geometric progression is 49 2 So,common ratio Here r   =   2 and let common difference =   d And we know that, a 2 = a 1 + d × 2 2 = a 1 + 2 d × 2 2   . . . . . . . . . . i a 3 = a 1 + 3 d × 2 3 a 4 = a 1 + 4 d × 2 4 Now adding all above equations we get, 31 a 1 + 98 d = 49 2   . .