An AP consists of 37 terms. The sum of the three middle most terms is 225 and the sum of the last three is 429. Find the AP.

Question

An AP consists of 37 terms. The sum of the three middle most terms is 225 and the sum of the last three is 429.  Find the AP.

Filo · Accepted Answer

Let a,d and n be the first term, common difference and the no. of terms of given AP.

Here

n = 37

so middle most term is

\frac{n + 1}{2}

\Rightarrow \frac{37 + 1}{2} \Rightarrow 1 8^{t h}

∴

three middle most terms are

1 8^{t h}, 1 9^{t h}, 2 0^{t h}

a_{18} + a_{19} + a_{20} = 225 \Rightarrow a + 17 d + a + 18 d + a + 19 d = 225

\Rightarrow 3 a + 54 d = 225

...(1)

last three terms are

3 5^{t h}, 3 6^{t h}, 3 7^{t h}

a + 34 d + a + 35 d + a + 36 d = 429

\Rightarrow 3 a + 105 d = 429

...(2)

subtracting (1) from (2), we get

51 d = 204

\Rightarrow d = 4

putting

d

in (1), we get

3 a + 54 \times 4 = 225

3 a = 225 - 216 \Rightarrow a = 3

Therefore the AP is

a, a + d, a + 2 d, a + 3 d, ....

i.e

3, 7, 11, 15......

Question Text	An AP consists of $37$ terms. The sum of the three middle most terms is $225$ and the sum of the last three is $429$ . Find the AP.
Answer Type	Text solution:1
Upvotes	150

An AP consists of $37$ terms. The sum of the three middle most terms is $225$ and the sum of the last three is $429$ . Find the AP.