Let s 1 , s 2 , s 3 . . . . , s 10 respectively be the sum of 12 terms of 10 A . Ps whose first terms are 1 , 2 , 3 , . . . . , 10 and the common differences are 1 , 3 , 5 , . . . , 19 respectively. Then ∑ i = 1 10 s i is equal to

Step-by-step solution

Given, First term of A.P are 1 , 2 , 3 . . . . 10 , so general term of the first term will be i And common difference are 1 , 3 , 5 , . . . . , so general term of common difference is given by 2 i - 1 Now sum of the A.P is given by, S i = 12 2 2 × i + 12 - 1 2 i - 1 ⇒ S i = 6 2 × i + 11 2 i - 1 ⇒ S i = 144 i - 66 So, ∑ i = 1 10 S i = ∑ i = 1 10 144 i - 66 ∑ i = 1 10 1 ⇒ ∑ i = 1 10 S i = 144 10 × 11 2 - 66 × 10 ⇒ ∑ i = 1 10 S i = 792 10 - 66 &