Question

if sum of 7term is 49 and the sum of 17term is 289 then find the sum of nth terms

Answer 1

Answer:

Step-by-step explanation: GIVEN :

S7=49

S17 =289

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

there fore : S7=7/2[2a+(7-1)d

49=7/2[2a+6d]

98=7[2a+6d]

98/7=[2a+6d]

14=2a+6d  ...........eq 1

S17=17/2[2a+(17-1)d]

289=17/2[2a+16d]

578/17=2a +16d

34=2a+16d............eq2

now divide eq 1 by 2

we get : a+3d=7..........eq3

now divide eq 2 by 2

we get: a + 8d=17.....eq4

now substract eq 3 from eq 4

we get:d=2

now put d=2 in eq 3

a+6=7

a=7-6

a= 1

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

put value of a and d in this formula

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

Sn=n/2[2+2n-2]

Sn=n/2[2n]

Sn=n2