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Arithmetic Progressions

Short Answer Type

41.

Find the number of terms in each of the following APs :

$space space space 18 comma space 15 1 half comma space 13 comma space....... comma space minus 47$

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42.
Check whether – 150 is a term of the AP : 11, 8, 5, 2 . .

The given list of number is
11, 8, 5, 2,.....
a₂ – a_x = 8 – 11 = –3
a₂ – a₂ = 5 – 8 = –3
And, a₄ – a₃ = 2 – 5 = –3
i.e., a_{k + 1} – a_k is the same every time. So, the given list of numbers form an A .P. with first term a = 11 and the common difference d = –3.
Let –150 be the nth term of the given A .P.
Then, a_n= -150
$The given list of number is11, 8, 5, 2,.....a2 – ax = 8 – 11 =$ $rightwards double arrow$ a + (n - 1)d = - 150
$rightwards double arrow$ 11 + (n - 1) (-3) = - 150

$rightwards double arrow space$ -3(n - 1 ) = - 150 -11
$rightwards double arrow$ -3 (n - 1) = -161
$rightwards double arrow$ 3 ( n - 1) = - 161
$rightwards double arrow$ 3(n - 1) = 161

$rightwards double arrow space space straight n minus 1 equals 161 over 3$

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