Question

if the sum of first 7 term of an ap is 49 and that of 17th term is 289 find the sum of first n terms ​

Answer 1

Answer:

Step-by-step explanation:

Sum of first 7 terms = 49

s7=49

(n/2)(2a1+(n-1)d)=49

7(2a1+6d)=98

14(a1+3d)=98

a1+3d=7--->1

sum of 17th term is = 289

s17=289

(n/2)(2a1+(n-1)d)=289

(17/2)(2a1+16d)=289

17(a1+8d)=289

a1+8d=17--->2

eq 2 - eq 1 --->

a1+8d=17

a1+ 3d=7

-----------------

5d=10

d=2

put d=2 in eq 1

a1=7-3d

a1=7-3(2)

a1=7-6

a1=1

a1=1,d=2

Then AP ---> 1,3,5,7,9,11,13,15,17,19,21,...,n

sum of first n terms

sn=(n/2)(2a1+(n-1)d)

=(n/2)(2+(n-1)2)

=(n/2)(2+2n-2)

=(n/2)(2n)

=n*n

=n²