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

(i) An AP 5, 12, 19, ... has 50 terms. Find its last term. Hence, find the sum of its last 15 terms. [CBSE 2015]

(ii) An AP 8, 10, 12, ... has 60 terms. Find its last term. Hence, find the sum of its last 10 terms. [CBSE 2015]

Open in App
Solution

(i) The given AP is 5, 12, 19, ... .

Here, a = 5, d = 12 − 5 = 7 and n = 50.

Since there are 50 terms in the AP, so the last term of the AP is a50.

l=a50=5+50-1×7 an=a+n-1d =5+343 =348

Thus, the last term of the AP is 348.

Now,

Sum of the last 15 terms of the AP

=S50-S35=5022×5+50-1×7-3522×5+35-1×7 Sn=n22a+n-1d=502×10+343-352×10+238=502×353-352×248

=17650-86802=89702=4485

Hence, the required sum is 4485.

(ii) The given AP is 8, 10, 12, ... .

Here, a = 8, d = 10 − 8 = 2 and n = 60

Since there are 60 terms in the AP, so the last term of the AP is a60.

l=a60=8+60-1×2 an=a+n-1d =8+118 =126

Thus, the last term of the AP is 126.

Now,

Sum of the last 10 terms of the AP

=S60-S50=6022×8+60-1×2-5022×8+50-1×2 Sn=n22a+n-1d=30×16+118-25×16+98=30×134-25×114
=4020-2850=1170

Hence, the required sum is 1170.

flag
Suggest Corrections
thumbs-up
1
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Introduction to AP
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon