Question

In an ap the first term is 2 and sum of first 5 term is 1/4 of the next 5 term prove that a 20 =-112​

Answer 1

Step-by-step explanation:

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

□a=2

$\huge{\boxed{\boxed{\underline{\sf{TO\:PROVE-}}}}}$

☆a=-112

>>According to given question

$(a1 + a2 + a3 + a4 + a5) = \frac{1}{4} (a6 + a7 + a8 + a9 + a10) \\ according \: t o \: formula \\ = ) \frac{5}{2}(2a + (5 - 1)d = \frac{1}{4} \times \frac{5}{2}(2a6 + (5 - 1)d) \\ = ) \frac{5}{2} (2a + 4d) = \frac{1}{4} \times \frac{5}{2} (2 a6 + 4d) \\ = )8a + 16d = 2(a + 5d) + 4d \\ = )8a + 16d = 2a + 10d + 4d \\ = )6a = 14d - 16d \\ = )6 \times 2 = - 2d \\ = )12 = - 2d \\ = )d = \frac{ - 12}{2} \\ = )d = - 6$

□d=-6

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

$\huge{\boxed{\boxed{\underline{\sf{PROVED}}}}}$

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