Question

6. The first and the last terms of an AP are 17 and 350 respectively. If the common difference
is 9, how many terms are there and what is their sum?​

Answer 1

Answer:

Step-by-step explanation: Given: a=17 , l = 350 ,d =9

we can use formula sum=n/2(a+l) ⇒ =n/2(17+350) ⇒ sum= 367 (n/2)....... (i)           also , sum= n/2(2a+(n-1)d) ⇒ = n/2 (2×17+(n-1)9) ⇒ =n/2 (34 +9n-n) ⇒      sum= n/2(25+9n)...........(ii)                                                                                      from i & ii , 367 × n/2 = n/2 (25+9n) ⇒ 367 = 25 + 9n ⇒ n =38 putting value in (i) , sum= 367 × 38/2 = 6973

Answer 2

Sᴏʟᴜᴛɪᴏɴ :

• Given A.P in which a = 17
• Last term = l = 350
• Common difference, d = 9

We know that,

an = a + (n - 1) d

⇒ 350 = 17 + (n - 1) 9

⇒ 350 = 17 + 9n - 9

⇒ 9n = 350 - 8

Sn = n/2[a + l]

⇒ S38 = 38/2[17 + 350]

⇒ S38 = 19 × 367

⇒ S38 = 6973

Hence,

• n = 38
• Sn = 6973