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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 . .

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43.

Find the 31st term of an AP whose 11th term is 38 and the 16th term is 73.

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44.

An AP consists of 50 terms of which 3rd term is 12 and the last term is 106. Find the 29th term.

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45. If the 3rd and 9th terms of an A .P. are 4 and -8 respectively, which term is zero?

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46. The 17th term of an A .P. exceeds the 10th term by 7. Find the common difference.

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47.
Which term of the AP : 3, 15, 27, 39, . . . will be 132 more than its 54th term?

Given A.P. is : 3, 15,27,39.....
Here a₁ = 3, a₂ = 15
a₃ = 27, a₄ = 39
d = a₂ – a₁ = 15 – 3 = 12
a₅₄ = a (54 – 1)d
= 3 + 53 x 12
= 3 + 636 = 639
Let ntn term be 132 more than a₅₄We know that,
a_n= a + (n - 1)d
a₅₄ + 132 = a + (n - 1)d
$rightwards double arrow$ 639 + 132 = 3 + (n - 1) x 12
$rightwards double arrow$ 771 - 3 = 12(n - 1)
$rightwards double arrow space$ 768 = 12(n - 1)
$rightwards double arrow space straight n minus 1 equals 768 over 12 equals 64 rightwards double arrow space straight n space equals space 64 space plus space 1 space equals space 65$