If 6^{\;{th }\;} and 13^{\;{th }\;} term of an A.P are 15 and 36 respectively the A.P is

Correct Answer is : 0,3,6,90,3,6,90,3,6,9

Correct Answer is : 0,3,6,90,3,6,90,3,6,9

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Sequence and Series

Question : 80 of 86

Marks: +1, -0

6^{\;\text{th }\;}

13^{\;\text{th }\;}

term of an A.P are 15 and 36 respectively the A.P is

Solution:

Concept:

For an arithmetic progression (A.P.),

n^{\text{th}}

term is

T_n = a + (n-1)d

, where

a

is first term and

d

is common difference.

Explanation:

Given

T_6 = a + 5d = 15

and

T_{13} = a + 12d = 36

Subtracting first from second:

(a + 12d) - (a + 5d) = 36 - 15 \implies 7d = 21 \implies d = 3

Substitute

d = 3

a + 5(3) = 15 \implies a + 15 = 15 \implies a = 0

Thus the A.P. is

0, 3, 6, 9, \dots

Answer:

Option D:

0, 3, 6, 9

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