Question

if the sum of the first 7 terms of an AP is 63 and the sum of the 17 terms is 289,find the sum of the first n terms​

Answer 1

Answer:

The Answer is as Follows

Step-by-step explanation:

Using Formula :-

1) Sñ = n/2[2a+(n-1)d]

Answer 2

S7=63

or

7/2 [2a + (7-1) d] = 63

7[2a+ 6d] = 126

14a + 42d = 126

7a+21d=63

a+3d=9

7a+21d=63

a+3d=9 -EQ 1

s17=289

or

17/2[2a+(17-1)d] = 289

17[2a+16d]= 578

34a+272d=578

17a+136d=289

a+8d=17 EQ-2

solving EQ 1 AND 2

a = 21/5 and d = 8/5

then sum of first n terms of ap = Sn

Sn= n/2[2a+(n-1)d]

n/2 [2×21/5+(n-1)8/5]

HENCE

SN = n/2 [ 42/5 +(n-1) 8/5 ]

HOPE IT HEPLS.