Question

a) The first term of an arithmetic series is 32 with common difference 8. Find
sum of first 8 terms.
on difference is 6. Find the first 8 terms​

Answer 1

Step-by-step explanation:

We know that the general term of an arithmetic progression with first term a and common difference d is Tn=a+(n−1)d

It is given that the 3rd term of the arithmetic series is 7 that is T3=7 and therefore, 

T3=a+(3−1)d⇒7=a+2d....(1)

Also it is given that the 7th term is 2 more than three times its 3rd term that is 

T7=(3×T3)+2=(3×7)+2=21+2=23

Thus, 

T7=a+(7−1)d⇒23=a+6d....(2)

Subtract equation 1 from equation 2:

(a−a)+(6d−2d)=23−7⇒4d=16⇒d=416⇒d=4

Substitute the value of d in equation 1:

a+(2×4)=7⇒a+8=7⇒a=7−8=−1

We also know that the sum of an arithmetic series with first term a and common difference d is Sn=2n[2a