The sum 2 × 5+5 × 9+8 × 13+ ldots 10 terms is

Question

The sum 2 × 5+5 × 9+8 × 13+ ldots 10 terms is (A) 4500 (B) 4555 (C) 5454 (D) None of these

Tardigrade Admin · Accepted Answer

S =2 × 5+5 × 9+8 × 13+ ldots 10 text terms tr =(3 r-1)(4 r+1) =12 r2-r-1 ∴ S= displaystyle∑r=110(12 r2-r-1) =12 (10 ⋅ 11 ⋅ 21/6)-(10 ⋅ 11/2)-10 =10(462-(11/2)-1) =4555

Q. The sum $2 \times 5 + 5 \times 9 + 8 \times 13 + \dots 10$ terms is

4500

4555

5454

None of these

$S = 2 \times 5 + 5 \times 9 + 8 \times 13 + \dots 10 terms$
$t_{r} = (3 r - 1) (4 r + 1)$
$= 12 r^{2} - r - 1$
$∴ S = r = 1 \sum 10 (12 r^{2} - r - 1)$
$= 12 \frac{10 \cdot 11 \cdot 21}{6} - \frac{10 \cdot 11}{2} - 10$
$= 10 (462 - \frac{11}{2} - 1)$
$= 4555$

Q. The sum 2×5+5×9+8×13+…10 terms is