If the nth terms of two A.P.s 23, 25, 27, ... and 5,8,11,14...are equal then find the value of n
Answers
Answer:
Step-by-step explanation:
Formula for finding is a+(n-1)d
As they are equal put the values in formula
23+2n-2 = 5+3n-3
21+2n=2+3n
n=19
value of n = 19
first AP⇒ 23, 25, 27, .....
first term, a = 23 and common difference,d = 2
so, nth term , Tn = a + (n - 1)d
= 23 + (n - 1) × 2 = 23 + 2n - 2 = 21 + 2n ......(1)
2nd AP ⇒5, 8, 11, 14 ........
first term, a = 5 and common difference, d = 3
nth term, T'n = a + (n - 1)d
= 5 + (n - 1) × 3
= 5 + 3n - 3 = 2 + 3n ...........(2)
from equations (1) and (2) we get,
21 + 2n = 2 + 3n
⇒21 - 2 = 3n - 2n
⇒n = 19
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