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

Question 6
The 26th, 11th and the last terms of an AP are 0, 3 and 15, respectively. Find the common difference and the number of terms.

Open in App
Solution

Let the first term, common difference and number of terms of the AP are a, d and n, respectively.
We know that, if last term of an AP is known, then,
l = a + (n - 1)d . . . . . (i)
And nth term of an AP is,
Tn = a + (n - 1)d . . . . . (ii)
Given that, 26th term of an AP = 0
T26=a+(261)d=0 [from eq.(i)]
a + 25d = 0 . . . . (iii)
11th term of an AP = 3
T11=a+(111)d=3 [from eq.(ii)]
a + 10d = 3 . . . . .(iv)
Last term of the AP, l=15
l = a + (n - 1)d [From eq. (i)]
+15 = a + (n - 1)d . . . . . (v)
Now, subtracting eq.(iv) from eq.(iii),
a+25d=0a+10d=3 –––––––––––15d=3
d=15
Put the value of d in eq.(iii), we get;
a+25(15)=0 a5=0a=5
Now, put the value of a, d in eq.(v), we get;
15=5+(n1)(15)
-1 = 25 - (n - 1)
-1 = 25 - n + 1
n = 25 + 2 = 27
Hence, the common difference and number of term are 15 and 27, respectively.

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
Join BYJU'S Learning Program
CrossIcon