Question

find the sum to n terms of the series
${5}^{2} + {6}^{2} + {7}^{2} + ...... {20}^{2}$

Answer 1

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Answer 2

⭕️In the question;
the given series is :-
5^2+6^2+7^2+........20^2

⭕️We have to find the nth term.

✔️✔️logic here is that :-
"Each term in this series is square of a no. "

⭕️Sequence is an A.P.

⭕️nth term is 5+(n−1)×1

⭕️the nth term of an A.P. is
=a+(n−1)da+(n−1)d

⇒4+n=20

⇒4+n=20 

✴️✴️or ✴️✴️

n=16n=16

i.e.

The number of terms in the given series is 1n=16
n=16

∴∴ The nthnth term of the given series is :-

tn=(4+n)^2

⇒tn=16+n2+8n

✔️✔️now.. for more simplification refer attachment above !