an ap has 23 terms the sum of midle term is 720 and sum of last3 term of apis 1320 what is 18 th term .A=240
Answers
Answer:
360
Step-by-step explanation:
Number of terms n = 23
Let first term = a
and common difference = d
after removing middle 3 terms, number of terms left = 23 - 3 = 20
= 10 terms are present to the left of middle 3 terms and 10 terms are present to the right of middle 3 terms ( Since, 20/2 = 10)
= Three middle terms are 11th, 12th and 13th terms
= Three middle terms are a + (11 - 1)d, a + (12 - 1)d and a (13 - 1)d
= Three middle terms are a + 10d, a + 11d and a + 12d
Therefore, a + 10d + a + 11d + a + 12d = 720
= 3a + 33d = 720............ = 3(a + 11d) = 720
= a + 11d = 720/3............ = a + 11d = 240
Last three terms are 21st, 22nd and 23rd terms
= Last three terms are a + (21 - 1)d, a + (22-1)d and a + (23-1)d
= Last three terms are a + 20d, a + 21d, and a + 22d
Therefore, a + 20d + a + 21d + a + 22d = 1320
= 3a + 63d = 1320.......... = 3(a + 21d) =1320
= a + 21d = 1320/3......... = a + 21d = 440
Subtracting (1) from (2)
a + 21d = 440
a + 11d = 240
------------------------------
0a + 10d =200
= 10d = 200............... = d = 20/10........... = d = 20.
Putting d = 20 in (1)
a + 11 * 20 = 240
= a + 220 = 240.......... = a = 240 - 220.......... = a = 20
18th term of A.P. = a + (18 - 1)d = a + 17d
= 20 + 17 * 20 = 20 + 340 = 360.
the answer is 32
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