Question

the sum of n terms of an ap is 136 and common difference is 4 if the last term is 31 then find the number of terms

Answer 1

Answer:

n=8

Step-by-step explanation:

S

n

=

2

n

{2a+(n−1)d}

a+(n−1)d=31⇒a=31−4(n−1)

∴136=

2

n

{2[31−4(n−1)]+(n−1)d}

n[70−8n+4n−4]=272

n(66−4n)=272

4n

2

−66n+272=0

2n

2

−33n+136=0

2n(n−8)−17(n−8)=0

(2n−17)(n−8)=0

∴n=8