Question

how many terms of the series 2+4+6... amount to 42​

Answer 1

Answer:

6 terms

Step-by-step explanation:

First term, a = 2

difference of second and first term, d = 2

number of terms, n

formula for sum of A.P

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

42= n/2[2(2)+(n-1)2]

    =n/2[4+2n-2]

    =n/2[2n+2]

    =n[n+1]

    =n²+n

then by solving the quadratic eq.,

n²+n-42=0

n²-6n+7n-42=0

n(n-6)+7(n-6)=0

(n-6)(n+7)=0

n-6=0 or n+7=0

n=6 or n= -7

We will not consider the negative number of terms.

So, the answer is 6.

Answer 2

Answer:

6 Term

Step-by-step explanation:

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

42= n/2[2(2)+(n-1)2]

42= n/2[4+2n-2]

42= n/2[2n+2]

42= n[n+1]

then by solving the quadratic eq., n?n(n-6)+7(n-6)=0

(n-6)(n+7)=0

n-6=0 or n+7=0

n=6 or n= -7

We will not consider the negative number of terms. So, the answer is 6.