Question

Find the A.P whose 10th term is 5 and 18th term is 77

Answer 1

a = -76
A.P. = -76,-76+9,-76+2(9).....
A.P.= -76,-67,-58....................

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Answer 2

Given:

a(10) = 5.

a(18) = 77.

To Find:

The A.P.

Solution:

According to the formula,

a(10) = a + 9d = 5 ---------(i).

a(18) = a + 17d = 77 ------------(ii).

Subtracting equation (i) from equation (ii),

a + 17d = 77.

-a - 9d = -5.

0 + 8d = 72.

8d = 72.

d = 72/8.

d = 9.

Putting value of d in equation (i),

a + 9*9 = 5.

a + 81 = 5.

a = 5 - 81.

a = -76.

So,

The A.P. will be,

-76, (-76 + 9), (-76 + 2(9)), so on.

= -76, -67, -58, -49, -40, -31, so on.

Hence, the A.P. is -76, -67, -58, -49, -40, -31, so on.