Questions based on pattern

1. Observe the following pattern

(1×2) + (2×3) = (2×3×4)/3

(1×2) + (2×

Questions based on pattern

1. Observe the following pattern

(1×2) + (2×3) = (2×3×4)/3

(1×2) + (2×3) + (3×4) = (3×4×5)/3

(1×2) + (2×3) + (3×4) + (4×5) = (4×5×6)/3

And find the value of

(1×2) + (2×3) + (3×4) + (4×5) + (5×6)

2. Observe the following pattern

1 = 1/2 (1×(1+1))

1+2 = 1/2 (2×(2+1))

1+2+3 = 1/2 (3×(3+1))

1+2+3+4 = 1/2 (4×(4+1))

And find the values of each of the following:

(i) 1+2+3+4+5+…+50

(ii) 31+32+….+50

3. Observe the following pattern
12 = 1/6 (1×(1+1)×(2×1+1)))
12+22 = 1/6 (2×(2+1)×(2×2+1)))
12+22+32 = 1/6 (3×(3+1)×(2×3+1)))
12+22+32+42 = 1/6 (4×(4+1)×(2×4+1)))

And find the values of each of the following:

(i) 12+22+32+42+…+102

(ii) 52+62+72+82+92+102+112+122 Class 8 mathematics chapter 6 square and square root​