Question

sum of first 25 terms of an AS is 56 what is it's 13 term​

Answer 1

Step-by-step explanation:

Let the A.P. be a,a+d,a+2d,a+

3d,...a+(n−2)d,a+(n−1)d.

Sum of first four terms =a+(a+d)+

(a+2d)+(a+3d)=4a+6d

Sum of last four terms

=[a+(n−4)d]+[a+(n−3)d]+

[a+(n−2)d]+[a+(n−1)d]⇒=4a+

(4n−10)d

According to the given condition, 4a+6d=56

6d=56

⇒4(11)+6d=

56[Since=11(given)

⇒6d=12⇒d=2

∴4a+(4n−10)d=112

⇒4(11)+(4n−10)2=112

⇒(4n−10)2=68

⇒4n−10=34

⇒4n=44⇒n=11

Thus the number of terms of A.P. is 11.

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