An ap consists up of 37 terms. The sum of the middlemost terms is 225 and the sum of the last three terms of an ap is 120 . Find the AP
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Answer:
3,7,11,15,19,…………..147
Step-by-step explanation:
Since there are 37 terms. So, middle most term = (37 + 1)/2 = 19th term
=> 3 middle most terms are
18th, 19th & 20th
a = first term : d = common difference
T18 = a + 17d
T19 = a + 18d
T20 = a + 19d
=> 3a + 54 d = 225 …….. (1)
Now, last 3 terms..
T35 = a+ 34d
T36 = a + 35d
T37 = a + 36d
=> 3a + 105d = 429 ………….. (2)
Eq (1) - eq(2)
51d = 204
=> d = 4
Hence, 3a + 216 = 225
=> a = 3
So, AP is…
3,7,11,15,19,…………..147
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Answer:
3,7,11,15...
Step-by-step explanation:
Total number of terms = 37.
(i) Sum of middlemost terms is 37.
The AP consists of 37 terms(odd).
So, (37 + 1)/2 = 19th term.
So, the middlemost terms are 18th, 19th,20th terms.
∴ t₁₈ + t₁₉ + t₂₀ = 225
nth term of an AP tn = a + (n - 1) * d
⇒ (a + 17d) + (a + 18d) + (a + 19d) = 225
⇒ 3a + 54d = 225
⇒ a + 18d = 75
(ii) Sum of last three terms is 120.
∴ t₃₅ + t₃₆ + t₃₇ = 120
nth term of an AP tn = a + (n - 1) * d.
⇒ a + 34d + a + 35d + a + 36d = 120
⇒ 3a + 105d = 120
⇒ a + 35d = 40
On solving (i) & (ii), we get
a + 18d = 75
a + 35d = 40
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-17d = 35
d = 35/-17
Your Question seems to be incorrect.
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Consider sum of last three terms as 429.
⇒ a + 34d + a + 35d + a + 36d = 429
⇒ 3a + 105d = 429
⇒ a + 35d = 143. --------- (iii)
On solving (i) & (iii), we get
a + 18d = 75
a + 35d = 143
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-17d = -68
d = 4
Substitute d = 4 in (i), we get
⇒ a + 18d = 75
⇒ a = 3.
Therefore, the AP is 3,7,11,15,....
Hope it helps!