Question

The sum of first 5 terms of an arithmetic sequence is 35 and

the sum of first 9 terms is 99

a) What is its third term ?

b) What is its common difference ?

c) What is the algebraic form of this sequence ?​

Answer 1

Answer:

a. 7

b. 2

c. 2n+1

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Answer 2

GIVEN,,,,,,

S5= 35

S9 = 99

So,,,,,after solving formula ,we get------

35 = 5/2(2a + (5-1)d)

70 = 5(2a + 4d)

14 = 2(a + 2d )

7 =a + 2d

a = 7-2d________ eq. (1)

99 = 9/2(2a + (9-1)d)

198 = 9(2a + 8d)

22= 2(a + 4d)

11 = a + 4d

11 = 7 - 2d + 4d

2d = 4

d = 2.

So,,,, a = 7-2(2)

a = 7-4 = 3

a) a3 = a+2d = 3+2(2) = 3+4 = 7..

b) common difference = 2..

c) A.P. = 3,5,7,9,11,13,.............

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