Question

evaluate 3+5+7+6+9+12+9+13+17........to30terms

Answer 1

The given sequence i.e., 3 + 5 + 7 + 6 + 9 + 12 + 9 + 13 + 17 +..... to 30 terms.

can be rewritten as 3 + 6 + 9 + .... to 10 terms + 5 + 9 + 13 + .... to 10 terms + 7 + 12 + 17 + .... to 10 terms

clearly all these sequence forms an A.P. having 10 terms with first terms 3, 5, 7 and common difference 3, 4, 5

Hence, required sum =10/2[2 × 3 + (10 - 1)3] +10/2[2 × 5 + (10 - 1)4] +10/2[2 × 7 + (10 - 1)5]

= 5(6 + 9 × 3) + 5(10 + 9 × 4) + 5(14 + 9 × 5) = 5(6 + 27 + 10 + 36 + 14 + 45)

= 5 × 138 = 690

Answer 2

The given sequence i.e., 3 + 5 + 7 + 6 + 9 + 12 + 9 + 13 + 17 +..... to 30 terms.

can be rewritten as 3 + 6 + 9 + .... to 10 terms + 5 + 9 + 13 + .... to 10 terms + 7 + 12 + 17 + .... to 10 terms

clearly all these sequence forms an A.P. having 10 terms with first terms 3, 5, 7 and common difference 3, 4, 5

Hence, required sum =[2 × 3 + (10 - 1)3] +[2 × 5 + (10 - 1)4] +[2 × 7 + (10 - 1)5]

= 5(6 + 9 × 3) + 5(10 + 9 × 4) + 5(14 + 9 × 5) = 5(6 + 27 + 10 + 36 + 14 + 45)

= 5 × 138 = 690