Question

Q18. The sum of the first N terms of an arithmetic series, S, is 292 The 2nd term of S is 8.5 The 5th term of Sis 13 Find the value of N. Show clear algebraic working.​

Answer 1

Step-by-step explanation:

Sn= a+[n-1]d

S2= a+[2-1]d

8.5 = a+d _______Equation 1

S5 = a+[5-1]d

13=a+4d ________Equation 2

Subtract Equation 1 from Equation 2

13=a+4d

-

8.5= a+d

________

4.5= 3d

d=1.5

Substituting d=1.5 in equation 1

8.5=a+1.5

a=8.5-1.5

a=7

Sum of terms of an A.P =

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

292= n/2[2×7+(n-1)d]

292=n/2[14+(n-1)1.5

292×2=n[14+(n-1)1.5]

584=n[14+1.5n-1.5]

584= 14n+1.5n²-1.5n

584= 1.5n²+12.5n

1.5n²+12.5n-584

1.5n²-24n+36.5n-584

1.5n(n-16)+36.5(n-16)

(1.5n+36.5)(n-16)

**n-16=0

n=16