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The first and the last terms of an AP are 8 and 350 respectively. If its commondifference is 9, how many terms are there and what is their sum? |
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Answer» AP: 8.......350(Given) A1=8 An=350 D. =9 So the AP is, A2: a+d = 8+9=17 A3: a+2d = 8+2(9)=27 So we have the AP as 8,17, 26 Now we have to find number of terms present in the AP, Using An=a+(n-1)d 350=8+(n-1)9 350-8=(n-1)9 342/9=n-1 38=n-1 n=39 Now, we found out the number of terms, that is 39 terms in total. The next step is calculating the sum of all the 39 terms, so Using, Sn=n/2{2a+(n-1)d} Sn = 39/2{2(8)+(39-1)9} =39/2{16+342} =39/2*358 =6981 Therefore, we got the sum as 6981 Hope my answer helps you! Thank you. First term, a=8, Common Difference, d=9 Last Term, An= 350 a+(n-1)d= 350 8+(n-1)9=350 (n-1)9=350-8=342 (n-1)9= 342 n-1= 342/9= 38 n-1= 38 n= 38+1= 39, So, there are 39 terms. Sum of n terms, Sn=n/2(a+An) S39= 39/2(8+350) S39= (39/2) * 358 S39= 39* 179= 6981 a=8 An=350 d=9 An=? An=a+(n-1) d 350=8+(n-1) 9 350-8=(n-1) 9 342=(n-1) 9 38=n-1 38+1=n 39=n a=8 d=9 l=350 Sn=? Sn=n/2(a+l) S39=39/2(8+350) S39=39/2(358) S39=39(179) S39=6981 An= a+(n-1)d 350=8+(n-1)9 350-8=(n-1)9 342=(n-1)9 342/9=n-1 38=n-1 38+1=n 39=n Sn=n/2[a+an] Sn=39/2[8+350] Sn=39/2[358] Sn=39/2×358 Sn=39×179 Sn=6981 |
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