Question

in an ap the sum of first term ,thurs term and fivth term is 39 and sum of 2nd ,4 and 6 term is 51 find T20​

Answer 1

First term = a

third term = a + 2d

Fifth term = a + 4d

second term= a + d

4th term = a + 3d

6th term = a + 5d

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$a + a + 2d + a + 4d = > 39 \\ \\ 3a + 6d = > 39........(1) \\ \\ \\ a + d + a + 3d + a + 5d = > 51 \\ \\ 3a + 9d = > 51..........(2)$

By elimination method.

$3a + 6d = 39 \\ 3a + 9d = 51 \\ - - - - - - - \\ - \: \: \: \: \: \: - \: \: \: \: \: - \\ - - - - - - - \\ \: \: \: \: - 3d = - 12 \\ \\ d = \frac{12}{3} \\ \\ \boxed{d = 4}$

Put Value of d in (1) equation.

$a + 6(4) = 39 \\ \\ a + 24 = 39 \\ \\ a = 39 - 24 \\ \\ \boxed{a = > 15}$

Find 20th term ....

a20=???

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$\color{orange} \boxed{a20 = > a + (n - 1) \times d} \\ \\ a20 = 15 + (20 - 1) \times 4 \\ \\ a20 = 15 + 19 \times 4 \\ \\ a20 = 15 + 76 \\ \\ \boxed{ a20 = 91}$

The 20th term of AP = 91 ...

Hope it's helps you ☺️