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APWorksheet

This document contains two sections about arithmetic progressions (AP). Section A contains 9 problems about finding terms, sums, and properties of AP sequences. Section B contains 5 multiple choice questions related to AP, including finding sums of terms, identifying expressions for sums, and determining values based on AP properties.

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lakshay mittal
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68 views5 pages

APWorksheet

This document contains two sections about arithmetic progressions (AP). Section A contains 9 problems about finding terms, sums, and properties of AP sequences. Section B contains 5 multiple choice questions related to AP, including finding sums of terms, identifying expressions for sums, and determining values based on AP properties.

Uploaded by

lakshay mittal
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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Section (A) : Arithmetic Progression

A-1. In an A.P. the third term is four times the first term, and the sixth term is 17 ; find the series.

p
A-2. Find the sum of first 35 terms of the series whose pth term is + 2.
7

A-3. Find the number of integers between 100 & 1000 that are divisible by 7

A-4. Find the sum of all those integers between 100 and 800 each of which on division by 16 leaves
the remainder 7.

A-5. The sum of first p-terms of an A.P. is q and the sum of first q terms is p, find the sum of first (p
+ q) terms.

A-6. The sum of three consecutive numbers in A.P. is 27, and their product is 504, find them.

A-7. The fourth power of the common difference of an arithmetic progression with integer entries is
added to the product of any four consecutive terms of it. Prove that the resulting sum is the
square of an integer.

A-8. If a, b, c are in A.P., then show that:


(i) a2 (b + c), b2 (c + a), c2 (a + b) are also in A.P.
(ii) b + c − a, c + a − b, a + b − c are in A.P.

A-9. There are n A.M's between 3 and 54, such that the 8th mean: (n − 2)th mean:: 3: 5. The value
of n is.

Section (A) : Arithmetic Progression


A-1. The first term of an A.P. of consecutive integer is p2 + 1. The sum of (2p + 1) terms of this series
can be expressed as
(A) (p + 1)2 (B) (2p + 1) (p + 1)2 (C) (p + 1)3 (D) p3 + (p + 1)3
A-2. If a1, a2, a3, .... are in A.P. such that a1 + a5 + a10 + a15 + a20 + a24 = 225, then
a1 + a2 + a3 + ..... + a23 + a24 is equal to
(A) 909 (B) 75 (C) 750 (D) 900

A-3. If the sum of the first 2n terms of the A.P. 2, 5, 8, ....., is equal to the sum of the first n terms of
the
A.P. 57, 59, 61, ..., then n equals
(A) 10 (B) 12 (C) 11 (D) 13

A-4. The sum of integers from 1 to 100 that are divisible by 2 or 5 is


(A) 2550 (B) 1050 (C) 3050 (D) none of these

A-5. Let 6 Arithmetic means A1, A2, A3, A4, A5, A6 are inserted between two consecutive natural
number a and b (a > b). If A12 – A22 + A32 – A42 + A52 – A62 is equal to prime number then 'b' is
equal to
(A) 1 (B) 2 (C) 3 (D) 4
Section (A) :
A-1. 2, 5, 8,..... A-2. 160 A-3. 128 A-4. 19668 A-5. –(p + q) A-6. 4, 9,
14
A-9. 16
Section (A) :
A-1. (D) A-2. (D) A-3. (C) A-4. (C) A-5. (C)

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