Question

Find the sum of first 10 terms of A.P. whose nth term an = 9 - 5n.​

Answer 1

• Given: an=9−5n

• Taking n=1, 

a1=9−5(1)=9−5=4

• Taking n=2, 

a2=9−5(2)=9−10=−1

• Taking n=3, 

a3=9−5(3)=9−15=−6

• Therefore the series is 4,−1,−6,...

• So,a=4,d=a2−a1=−1−4=−5

• Now, we have to find the sum of the first 15th terms of the AP

• Sn=2n[2a+(n−1)d]

⇒Sn=215[2×4+(15−1)(−5)]

⇒S15=215[8−70]

⇒S15=215[−62]

⇒S15=15×(−31)

⇒S15=−465

=> Hence, the sum of 15th terms is −465.