EXERCISE 5.1 – Stepwise Solutions
1. Check whether the following form an AP
(i) Taxi fare: 15, 23, 31, 39, …
Step 1: Find differences.
23 – 15 = 8
31 – 23 = 8
39 – 31 = 8
Since difference is constant, it forms an AP.
(ii) Air removed each time:
Remaining air: 1, 3/4, 9/16, …
Differences are not equal.
Not an AP.
(iii) Cost of digging: 150, 200, 250, 300, …
Common difference = 50
Forms an AP.
(iv) Compound interest: 10000, 10800, 11664, …
Differences are not equal.
Not an AP.
2. Write first four terms
(i) a = 10, d = 10
10, 20, 30, 40
(ii) a = –2, d = 0
–2, –2, –2, –2
(iii) a = 4, d = –3
4, 1, –2, –5
(iv) a = –1, d = 1/2
–1, –1/2, 0, 1/2
(v) a = –1.25, d = –0.25
–1.25, –1.5, –1.75, –2
3. Find first term and common difference
(i) 3, 1, –1, –3
a = 3
d = 1 – 3 = –2
(ii) –5, –1, 3, 7
a = –5
d = 4
(iii) 1/3, 5/3, 9/3, 13/3
a = 1/3
d = 4/3
(iv) 0.6, 1.7, 2.8, 3.9
d = 1.1
4. Which are APs?
(i) 2, 4, 8, 16
Differences not equal → Not AP
(ii) 2, 5/2, 3, 7/2
d = 1/2 → AP
Next terms: 4, 9/2, 5
(iii) –1.2, –3.2, –5.2, –7.2
d = –2 → AP
Next: –9.2, –11.2, –13.2
(iv) –10, –6, –2, 2
d = 4 → AP
Next: 6, 10, 14
(v) 3, 3+√2, 3+2√2, 3+3√2
d = √2 → AP
Next: 3+4√2, 3+5√2, 3+6√2
(vi) 0.2, 0.22, 0.222
Differences not equal → Not AP
(vii) 0, –4, –8, –12
d = –4 → AP
Next: –16, –20, –24
(viii) –1/2, –1/2, –1/2
d = 0 → AP
(ix) 1, 3, 9, 27
Not AP
(x) a, 2a, 3a, 4a
d = a → AP
(xi) a, a², a³
Not AP
(xii) √2, √8, √18, √32
= √2, 2√2, 3√2, 4√2
d = √2 → AP
(xiii) √3, √6, √9, √12
Not AP
(xiv) 1², 3², 5², 7²
1, 9, 25, 49 → Not AP
(xv) 1², 5², 7², 73
Not AP