1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

# The first term of an arithmetic progression (A. P) is the common ratio of a GP and the first term of the same GP is the common difference of the AP. The sum of the first 10 terms of the AP is 155 and the sum of the first two terms of the GP is 9. Find the first term of the AP ?

A
5or17
No worries! Weâ€˜ve got your back. Try BYJUâ€˜S free classes today!
B
14
No worries! Weâ€˜ve got your back. Try BYJUâ€˜S free classes today!
C
2or252
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
22
No worries! Weâ€˜ve got your back. Try BYJUâ€˜S free classes today!
Open in App
Solution

## The correct option is C 2or252Let a,a+d....be the A.P and d,da,da2....be the G.PSum of n terms in AP is given as,Sn=n2[2a+(n−1)d]As per the question 102(2a+9d)=155......(1)Also, sum of first two terms ofGP is 9So As per question,d+da=9 ∴d(1+a)=9...................(2)Substituting d=91+a from equation 2 in equation 1 we get,102[2a+9(91+a)]=155∴2a+2a2+81=31+31a∴2a2−29a+50=0Solving above quadratic equation we get,a=252,a=2Hence first term of AP is a=252,a=2

Suggest Corrections
0
Join BYJU'S Learning Program
Related Videos
Geometric Progression
MATHEMATICS
Watch in App
Explore more
Join BYJU'S Learning Program