# The sum of first 13 terms of a.p. is 21 and the sum of first 21 terms is 13 . find the sum of the first 34 terms.

1
by gite

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by gite

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The sum of the first 21 terms is 21a + 210d = 13

Multiply the first equation by 21 and the second by 13.

273a + 1638d = 441

273a + 2730d = 169

Subtract.

1092d = -272

d = -68/273

Substitute into the first equation above.

13a -136/7 = 21

a = 283/91

So the nth sum is 283n/91 - 34n(n-1)/273.

Hence the sum of the first 34 terms is:

283*34/91 - 34*34*33/273

= 9622/91 - 12716/91

= -3094/91

= -34