The first term and the last term of an AP are 17 and 350 respectively. If the common difference is 9,how many terms are there and what is their sum?

Question

Izabelle Frost · Accepted Answer

Step 1GivenFirst term of A.P   (      a          1        )  =  17Last term of A.P   (      a          n        )  =  350Common defference   (  d  )  =  9Step 2finding the number of terms and their sum      a          n        =  350      a          1        +  (  n  −  1  )  d  =  350  17  +  (  n  −  1  )  9  =  350  (  n  −  1  )  9  =  350  −  17  (  n  −  1  )  9  =  333  (  n  −  1  )  =      333    9    n  −  1  =  37  =  37  +  1  =  37  +  1there are 38 terns in A.PWKTSome to n terns       S          n        =      n    2        [    a    +    1    ]    =      38    2        [    17    +    350    ]    =  19      [    367    ]    =  6973The sum to 38 terms=6973

Glenn Hopkins · Accepted Answer

Given:First term   (  a  )  =  17Last term   (  l  )  =      a          n        =  350and common difference   (  d  )  =  9  ∵      a          n        =  350  a  +  (  n  −  1  )  d  =  350  ⇒  17  +  (  n  −  1  )  9  =  350  ⇒  9  (  n  −  1  )  =  350  −  17  =  333  ⇒  n  −  1  =      333    9    =  37  ∴  n  =  38Now,       S          n        =      n    2    (  a  +  1  )  =      38    2    (  17  +  350  )  =  19  ×  367  =  6973Hence,   n  =  38 &amp;amp; sum of term       S          n        =  6973