Question

Find the 7th term of an a.s. If the sum of the first 13 terms is 416

Answer 1

Answer:

hey mate there's your answer

let first term of the AP be a1

and common difference be d .

we know that,

nth term of the AP is,

an=a1+(n-1)d

so 7th term of the AP is,

a7=a1+(7-1)d

a7=a1+6d __________(1)

Sum of n terms of AP is,

Sn=n/2[2a1+(n-1)d]

given sum of 13 terms of the AP is 416

S13=13/2[2a1+(13-1)d]

416 =13/2[2a1+12d]

416=13×2/2[a1+6d]

416=13[a1+6d]

416/13=a1+6d

32=a1+6d

a1+6d=32

a7=32 [ from eq.(1)]

so 7th term of the AP is a7=32

hope it helps you................

thank you!!!