Question

Match the following columns

Column I	Column II
(a) How many terms are there in the AP 8, 13, 18, 23,..., 163?	(p) 65
(b) 12th term from the end of the AP 9, 12, 15, 18, ..., 98 is	(q) 25
(c) The sum of the AP 5 + 12 + 19 + 26 + ... + 145 is	(r) 32
(d) The number of terms in the AP (−5) + (−1) + 3 + 7 + ... + 91 is	(s) 1575

Answer 1

(a) - (r), (b) -(p), (c) - (s), (d) - (q)

(a) a = 8, d = 5 and l = 163
T_n = a + (n − 1)d = 163
⇒ 8 + (n − 1) ⨯ 5 = 163

⇒ 5n = 160
⇒ n = 32

(b) l = 98 and d = 3
∴ 12^th term from the end of the AP = [l − (n - 1)d]
= 98 - 11​ ⨯ 3
= 98 - 33 = 65

(c) Here, a = 5, d = 7 and l = 145
T_n = 5 + (n - 1) ​⨯ 7 = 145
⇒ 7n = 147
⇒ n = 21
∴ S₂₁ = $\frac{n}{2}\left(a+l\right)=\left(\frac{21}{2}\right)\times \left(5+145\right)=21\times 75=1575$

(d) Here, a = -5, d = 4 and l = 91
​ T_n = 91
⇒ -5 + (n - 1) ​⨯ 4 = 91
⇒ 4n = 100
⇒ n = 25