Question

In an AP the first term is 2 and the sum of the first 5 term is one fourth the sum of the next five terms .Find 20th term

Answer 1

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Answer 2

Answer:

$\huge{\boxed{\boxed{\sf{a20=-112}}}}$

Step-by-step explanation:

$\huge{\boxed{\boxed{\underline{\sf{SOLUTION-}}}}}$

□a=2

$s5 = \frac{1}{4} (next \: sum \: of \: five \: term) \\ a1 + a2 + a3 + a4 + a5 = \frac{1}{4} (a6 + a7 + a8 + a9 + a10) \\ a + a + d + a + 2d + a + 3d + a + 4d = \frac{1}{4} (a + 5d + a + 6d + a + 7d + a + 8d + a + 9d) \\ = ) 5a + 10d = \frac{1}{4} (5a + 35d) \\ = ) (5a + 10d) \times 4 = 5a + 35d \\ = ) 20a + 40d = 5a + 35d \\ = )20a - 5a = 35d - 40d \\ = ) 15a = - 5d \\ = )15 \times 2 = - 5d \\ = ) 30 = - 5d \\ = ) d = \frac{30}{ - 5 } \\ = )d = - 6$

□d=-6

□a20=?

$a20 = a + 19d \\ \: \: \: \: \: \: \: \: = 2 + 19 \times - 6 \\ \: \: \: \: \: \: \: \: = 2 + ( - 114) \\ \: \: \: \: \: \: \: \: = 2 - 114 \\ \: \: \: \: \: \: \: \: = - 112$

$\huge{\boxed{\boxed{\sf{a20=-112}}}}$