Question

If the sum of first 7 terms of an AP is 49 and that of 17 terms is 289, Find the sum of first n Terms .​

Answer 1

Given:-

S7 = 49 .......eq(1)

S17 = 289 .....eq(2)

Solution :-

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

put the value of equation (1) in formula

49 = 7/2 + ( 2a + ( 7- 1)d )

49 = 7/2 + ( 2a + 6d)

7 = a + 3d ......... eq(3)

now put the value of equation (2)in formula

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

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

17 = a + 8d ........... eq(4)

solving equation (3) and equation(4) by elimination method....

17 = a + 8d

7 = a + 3d

then you got,

difference = 2

put the value of d in equation (1)

7 = a + 3 * 2

7 = a + 6

a = 7 - 6 = 1

first term a = 1

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Answer 2

Step-by-step explanation:

we know that

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

Sum of first 7 terms= 49

a=7-3d

Sum of first 17 terms=289

a=17-8d