Question

plz answer 3 and 4 questions

Answer 1

Hi...☺

Here is your answer...✌

3) :

$a_{10} = 46 \:\: \: \: \: \: ( given) \\ \\ a + 9d = 46 \\ \\ a = 46 - 9d \: \: \: \: \: .....(1)$
And,

$a_{5} + a_{7} = 52 \:\: \: \: \: \: ( given) \\ \\ a + 4d + a + 6d = 52 \\ \\ 2a + 10d = 52 \\ \\ \implies a + 5d = 26 \\ \\ \implies 46 - 9d + 5d = 26 \\ \\ \implies 46 - 4d = 26 \: \: \: \: \: \: \: [ from \: (1) ]\\ \\ \implies - 4d = - 20 \\ \\ \implies d = 5$

Putting d = 5 in (1) we get,

a = 46 - 9(5) = 46 - 45

=> a = 1

Therefore,

AP : 1 , 6 , 11 , 17 , .....

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4) :

$a_{4} = - 15 \:\: \: \: \: \: ( given) \\ \\ a + 3d = - 15 \\ \\ a = - 15 - 3d \: \: \: \: \: .....(2)$
And,

$a_{9} = - 30\:\: \: \: \: \: ( given) \\ \\ \implies a + 8d = - 30 \\ \\ \implies - 15 - 3d + 8d = - 30 \: \: \: \: \: \: \: [ from \: (2)]\\ \\ \implies 5d = - 30 + 15 \\ \\ \implies 5d = - 15 \\ \\ \implies d = - 3$

Putting d = -3 in (2) we get,

a = -15 - 3(-3) = -15 + 9

=> a = -6

Now,

$S_{10} = \frac{10}{2}[ 2 \times ( - 6) +9( - 3)] \\ \\ S_{10} = 5 \times ( - 12 - 27) \\ \\ S_{10} = 5 \times ( - 39) \\ \\ S_{10} = - 195$

Hence,

Sum of first 10 numbers is -195