The sum of all terms in a finite AP is 90 if first term is 2 and common difference is 8 then find number of terms and last term in this AP
Answers
Answer:
n=5
an=34
Step-by-step explanation:
sn =90
d= 8
a= 2
SN=[2a+(n-1) d] n/2
90=[2*2+(n-1) 8] n/2
90=[4+8n-8] n/2
90=4n+8n^2-8n
2
180 = 8n^2-4n
8n^2-4n-180=0
Step-by-step explanation:
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The common difference of AP is 3.
Step-by-step explanation:
Let the common difference of AP is d.
First term of an AP is 2.
nth term of an AP is
a_n=a+(n-1)d
The last term is 50.
50=2+(n-1)d
48=(n-1)d
.... (1)
Sum of n term of an AP is
S_n=\frac{n}{2}[2a+(n-1)d]
The sum of all these terms is 442.
442=\frac{n}{2}[2(2)+(n-1)d]
Using equation (1), we get442=\frac{n}{2}[4+48]
442=\frac{n}{2}(52)
442=26n
n=17
The value of n is 17. Put this value in equation 1.
48=(17-1)d
48=16d
d=3
Therefore the common difference of AP is 3.
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