wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

The number of terms of an A.P is even; the sum of the odd terms is 24, of the even terms 30, and the last term exceeds the first by 1012 find the sum of number of terms and 2nd term of the series ?

Open in App
Solution

Sum of all the terms is 24+30=54
Sum =n(2a+(n1)d)2 where a is the first term, d is the common difference, n is the number of terms.
Also, (n1)d=10.5
So, 54=n(2a+10.5)2
Also, 30=n(2a+(n1)d+d)4
i.e. 30=n(2a+10.5+d)4
we get 108=2an+10.5n and 120=2an+10.5n+dn
Subtracting the two, we have 12=dn
But ndd=10.5, implying d=1.5 & n=8
Also, 108=2an+10.5n=16a+84
a=1.5
Thus, second term = a+d=3
Hence 3+8 equals 11.

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Arithmetic Progression
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon