There are 60 terms in an AP. If its first and last term are 7 and 12

1.	There are 60 terms in an AP. If its first and last term are 7 and 125 respectively, then find its 32nd term.
Answer» Number of terms (n) = 60 First term (a) = 7 Last term (a_n) = 125 Formula, a_n = a + (n – 1)d ⇒ 125 = 7 + (60 – 1)d ⇒ 125 – 7 = 59 d ⇒ 118 = 59 d ⇒ d = 118/59 ⇒ d = 2 Thus, 32^nd term a₃₂ = a + (32 – 1)d = 7 + 31 × 2 = 7 + 62 = 69 Hence, 32^nd term of A.P. is 69.

There are 60 terms in an AP. If its first and last term are 7 and 125 respectively, then find its 32nd term.

Answer»

Number of terms (n) = 60

First term (a) = 7

Last term (a_n) = 125

Formula, a_n = a + (n – 1)d

⇒ 125 = 7 + (60 – 1)d

⇒ 125 – 7 = 59 d

⇒ 118 = 59 d

⇒ d = 118/59

⇒ d = 2

Thus, 32^nd term

a₃₂ = a + (32 – 1)d

= 7 + 31 × 2

= 7 + 62 = 69

Hence, 32^nd term of A.P. is 69.