How many terms of the AP:9,17,25,......,must be taken to get a sum of 450?
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given:
a=9
d=17-9
d=8
Sn=450
Sol:
Sn=n/2[2a+(n-1)d]
450×2=n[2(9)+(n-1)8]
900=n[18+8n-8]
900=n[10+8n]
900=10n+8n²
8n²+10n-900=0
by splitting middle term
8n²-80n+90n-900=0
8n[n-10]+90[n-10]=0
[8n+90]=0 or [n-10]=0
n=-90/80 or n=10
no. of terms cant be in -ve so n =10
a=9
d=17-9
d=8
Sn=450
Sol:
Sn=n/2[2a+(n-1)d]
450×2=n[2(9)+(n-1)8]
900=n[18+8n-8]
900=n[10+8n]
900=10n+8n²
8n²+10n-900=0
by splitting middle term
8n²-80n+90n-900=0
8n[n-10]+90[n-10]=0
[8n+90]=0 or [n-10]=0
n=-90/80 or n=10
no. of terms cant be in -ve so n =10
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