wiz-icon
MyQuestionIcon
MyQuestionIcon
7
You visited us 7 times! Enjoying our articles? Unlock Full Access!
Question

If the sum of first 7 terms of an AP is 49 and that of 17 terms is 289 then the common difference of the AP is

A
1
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
2
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
10
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
3
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is B 2
Let, 'a' be the first term and 'd' be the common difference of the AP.
Sum of n terms of an AP is:
n2×(2a + (n-1)d)
Sum of first 7 terms
= 72×(2a + (7-1)d)
= 72× (2a + 6d)
= 7 × (a+3d)
and Sum of first 17 terms
= 172×(2a + (17-1)d)
= 172× (2a + 16d)
= 17 × (a + 8d)
Given, Sum of first 7 terms = 49 and Sum of first 17 terms = 289
7 × (a+3d) = 49
a + 3d = 7 ......(1)
and, 17 × (a + 8d) = 289
a + 8d = 17.........(2)
Subtracting (1) from (2), we get
5d = 10
d = 2
Common difference of the given AP is 2.

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Formula for Sum of N Terms of an AP
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon