Question

If the sum of the first 7 terms of an A.P is 49 and that of 17 terms is 289. Then find the sum
of the first n terms.​

Answer 1

Step-by-step explanation:

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

49 = 7/2[2a +6(d) ].

98/7 = 2a +6d.......(1)

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

289 = 17/2 [2a +16(d) ].

478/17 = 2a +16d.......(2)

(2) - (1) =>

10d = 478/17 - 98/7

10d = 3348 - 1666/119

10d = 1682/119

d = 1.41

98/7 = 2a +6d

98/7 = 2a + 8.46

14 - 8.46 = 2a

a = 2.77

Sum of first n terms is=>

Sn = n/2 [5.54 + 1.41n - 4.13]

Sn = n/2 [4.13 + 1.41n]

Answer 2

Step-by-step explanation:

Let a and d respectively be the first term and common difference of the AP.

begin mathsize 12px style straight S subscript 7 space end subscript equals 49 space equals space 7 over 2 open parentheses 2 straight a space plus space 6 straight d close parentheses space rightwards double arrow space 7 space equals space straight a space plus space 3 straight d space space space space.... left parenthesis 1 right parenthesis

straight S subscript 17 space equals space 289 space equals space 17 over 2 open parentheses 2 straight a space plus space 16 straight d close parentheses space rightwards double arrow space 17 space equals space straight a space plus space 8 straight d space......... left parenthesis 2 right parenthesis

Solving space left parenthesis 1 right parenthesis space and space left parenthesis 2 right parenthesis comma space we space get

straight d space equals space 2 comma space straight a space equals space 1

straight S subscript straight n space equals space straight n over 2 open square brackets 2 cross times 1 space plus space open parentheses straight n minus 1 close parentheses cross times 2 close square brackets space equals space straight n squared end style