Arithmetic Progressions

1

Which term of the Arithmetic Progression –7, –12, –17, –22,... will be –82 ? Is –100 any term of the A.P. ? Give reason for your answer.

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2

How many terms of the Arithmetic Progression 45, 39, 33,... must be taken so that their sum is 180 ? Explain the double answer.

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3

The sum of first n terms of an AP is given by Sn = 2n2 + 3n. Find the sixteenth term of the AP.

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4

An AP consists of 37 terms. The sum of the three middle most terms is 225 and the sum of the last three terms is 429. Find the AP.

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5

In an A.P if sum of its first n terms is 3n2 + 5n and its kth term is 164, find the value of k.

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6

Find the sum of first 8 multiples of 3.

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7

The sum of four consecutive numbers in an AP is 32 and the ratio of the product of the first and the last term to the product of two middle terms is 7 : 15. Find the numbers.

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8

If the ratio of the sum of the first n terms of two A.Ps is (7n + 1) : (4n + 27), then find the ratio of their 9th terms.

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9

If the sum of the first 14 terms of an AP is 1050 and its first term is 10, find the 20th term.

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10

How many two-digit numbers are divisible by 3?

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11

Determine the AP whose 3rd term is 5 and the 7th term is 9.

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12

Find the 10th term of the AP: 2, 7, 12,...

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