Q. 254.4( 7 Votes )

# Observe the following pattern

And find the values of each of the following.

(i)

(ii)

Answer :

R.H.S = [(No. of terms in L.H.S) × (No. + 1) × (2 × No. + 1)]

(i) 1^{2} + 2^{2} + 3^{2} + 4^{2} + …… + 10^{2} = [10 (10 + 1) × (2 × 10 + 1)]

= [2310]

= 385

(ii) 5^{2} + 6^{2} +….. + 12^{2} = 1^{2} + 2^{2} + ….. 12^{2} – (1^{2} + 2^{2} + 3^{3} + 4^{2})

= [12 × (12 + 1) × (2 × 12 + 1)] - [4 ×(4 + 1) × (2 × 4 + 1)]

= 650 – 30

= 620

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If n is odd, then (1+3 +5 + 7 + ... to n terms) is equal to:

RS Aggarwal - MathematicsObserve the following pattern

And find the value of

(i) 100^{2}-99^{2} (ii) 111^{2}-109^{2}

(iii)99^{2}-96^{2}

Observe the following pattern

And write the value of 1+3+5+7+9+……… upto n terms.

RD Sharma - MathematicsObserve the following pattern

And find the values of each of the following.

(i)

(ii)

RD Sharma - MathematicsFind the value of each of the following, using the column method:

(96)^{2}

Find the value of each of the following, using the column method:

(52)^{2}