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Answer:

EXPLANATION.

3rd term of an Ap = 7. .........(1)

seventh term = 3 ( 3rd term) / 2.

To find the 20th term of an Ap.Nth term of an Ap.An = a + ( n - 1 )d.→ a + 2d = 7 ........... (1).

→ a + 6d = 3 ( a + 2d ) / 2.

→ 2 ( a + 6d ) = 3 ( a + 2d ).

→ 2a + 12d = 3a + 6d.

→ 12d - 6d = 3a - 2a.

→ 6d = a .......... (2).

put the value of equation (2) in (1).

we get,

→ 6d + 2d = 7.

→ 8d = 7.

→ d = 7/8.

put the value of D = 7/8 in equation (2)

we get,

→ 6 X 7/8 = a.

→ 21/4 = a.

→ First term = a = 21/4.→ Common difference = 7/8.20th term of an Ap.→ a + 19d.

→ 21/4 + 19 X 7/8.

→ 21/4 + 133/8.

→ 42 + 133 / 8.

→ 175/8.

20th term of an Ap = 175/8.
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