Question

13. An AP consists of 21 terms. If the sun
the sum of the last three terms is 237, then find the Al.
14. 852-832+842-822+832-8124822 802 is a series. Find the sum
series upto 30 terms.
then
15. In an AP, if m times the m th term is equal to n times the nt
find its (m+n) th term.
​

Answer 1

Answer:

15.

Step-by-step explanation:

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Answer 2

13)

Let a and d be the first term and common difference of the given A.P.

a 10 + a 11 + a 12 = 129

=> (a + 9d) + (a + 10d) + (a + 11d) = 129 [an = a + (n – 1)d]

=> 3a + 30d = 129

=> a + 10d = 43 … (1)

a 19 + a 20 + a 21 = 237

=> (a + 18d) + (a + 19d) + (a + 20d) = 237

=> 3a + 57d = 237

=> a + 19d = 79 … (2)

Solving (1) and (2), we get

a + 19d – a – 10d = 79 – 43

=> 9d = 36

=> d = 4

When d = 4, we get

a + 10 * 4 = 43

=> a = 43 – 40 = 3

Thus, the given A.P. is 3, 7, 11, 15…

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