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Arithmetic Progressions Final Assessment

Section A: Core Concepts

Question 1mcq
Which list is not an AP?
A.1,4,7,101,4,7,10
B.12,9,6,312,9,6,3
C.2,5,10,172,5,10,17
D.8,8,8,88,8,8,8
Question 2mcq
For −2,3,8,13,…-2,3,8,13,\ldots, what are aa and dd?
A.a=−2,d=5a=-2,d=5
B.a=5,d=−2a=5,d=-2
C.a=3,d=5a=3,d=5
D.a=−2,d=3a=-2,d=3
Question 3mcq
Find the 2020th term of 7,12,17,…7, 12, 17, \ldots.
A.9797
B.102102
C.107107
D.112112
Question 4mcq
Which term of 11,18,25,…11,18,25,\ldots is 9595?
A.1111th
B.1212th
C.1313th
D.1414th
Question 5mcq
If a4=16a_4=16 and a9=36a_9=36, find dd.
A.33
B.44
C.55
D.66
Question 6mcq
Which expression correctly represents the sum of first nn terms of an AP?
A.n2[2a+(n−1)d]\frac{n}{2}[2a+(n-1)d]
B.n2[2a+nd]\frac{n}{2}[2a+nd]
C.n[a+(n−1)d]n[a+(n-1)d]
D.d2[2n+(a−1)]\frac{d}{2}[2n+(a-1)]

Section B: Skill Practice

Question 7mcq
Find the sum of first 1515 terms of 2,6,10,…2,6,10,\ldots.
A.420420
B.450450
C.460460
D.480480
Question 8mcq
An AP has first term 99, last term 6969, and 1111 terms. Find the sum.
A.429429
B.439439
C.449449
D.459459
Question 9mcq
A student deposits ₹200200 in January and increases the deposit by ₹3030 each month. What is the deposit in the 1212th month?
A.₹500500
B.₹530530
C.₹560560
D.₹590590
Question 10mcq
A theater has 2525 seats in the first row and 33 more seats in each next row. How many seats are in row 1818?
A.7373
B.7676
C.7979
D.8282
Question 11mcq
A cycling plan covers 55 km on day 11, 77 km on day 22, 99 km on day 33, and so on. What is the total for 1010 days?
A.130130 km
B.140140 km
C.150150 km
D.160160 km
Question 12mcq
Insert two arithmetic means between 1010 and 2525.
A.13,1913,19
B.15,2015,20
C.14,2114,21
D.12,2212,22

Section C: Applications

Question 13mcq
The APs 4,10,16,…4,10,16,\ldots and 7,13,19,…7,13,19,\ldots have which relationship?
A.Every term is common.
B.No terms are common.
C.Only the first terms are common.
D.They have common difference 33.
Question 14mcq
A student says S4S_4 of 3,6,9,123,6,9,12 is 3333. Which check disproves it fastest?
A.3+6+9+12=303+6+9+12=30
B.12−3=912-3=9
C.3×12=363\times12=36
D.42=164^2=16
Question 15mcq
If an=6n−1a_n=6n-1, what is a25a_{25}?
A.144144
B.149149
C.150150
D.151151
Question 16mcq
An AP has first term aa and common difference 33. If the 77th term is 2828, find aa.
A.77
B.1010
C.1212
D.1515
Question 17mcq
The sum of the first nn terms of an AP is Sn=2n2+3nS_n=2n^2+3n. What is the first term?
A.33
B.55
C.77
D.1010
Question 18mcq
If a=4a=4, l=40l=40 and Sn=220S_n=220, find nn.
A.88
B.99
C.1010
D.1111

Section D: Mixed Challenge

Question 19mcq
A machine produces 120120 items on day 11 and 1515 more items each next day. How many items are produced in the first 88 days?
A.13201320
B.13801380
C.14401440
D.15001500
Question 20mcq
In a triangular seating pattern, rows contain 4,7,10,…4,7,10,\ldots chairs. If there are 1313 rows, how many chairs are there?
A.280280
B.286286
C.292292
D.298298
Question 21mcq
A reading schedule starts with 1212 pages and increases by 44 pages daily. How many pages are read on day 66?
A.2828
B.3030
C.3232
D.3636
Question 22mcq
If x,12,yx, 12, y are consecutive terms of an AP and x+y=30x+y=30, what is x+yx+y compared with twice the middle term?
A.It is less than 2424.
B.It equals 2424.
C.It is greater than 2424.
D.It cannot be determined.
Question 23mcq
Which term is common to 2,5,8,…2,5,8,\ldots and 4,9,14,…4,9,14,\ldots?
A.1414
B.1717
C.2020
D.2323
Question 24mcq
Which is the best way to check whether 2121 belongs to 3,7,11,…3,7,11,\ldots?
A.Check if 21−321-3 is divisible by 44.
B.Check if 21+321+3 is divisible by 44.
C.Check if 2121 is prime.
D.Check if 2121 is even.