Question

The 13th of an AP is 3 and the sum of first 13 terms is 234. FIND the common difference and the sum of first 21 terms

Answer 1

Answer:

Common difference = -2.5 and the sum of first 21 terms = 168 .

Step-by-step explanation:

We are given that the 13th of an AP is 3 and the sum of first 13 terms is 234.

Let the first term of an AP be denoted by a and common difference by d.

So, 13th of an AP is 3 which means;

               ⇒ $a_1_3$ = 3   ⇒ a + (13 - 1)*d = 3  {$\because$ $a_n = a + (n-1)d$ }

                                 ⇒ a + 12*d = 3

                                 ⇒ a = 3 - 12*d ------------ [Equation 1]

Also, sum of first 13 terms is 234 which means;

              ⇒ $S_1_3$ = 234  ⇒  $\frac{13}{2}[2a + (13-1)d]$ = 234 {$\because S_n = \frac{n}{2}[2a+(n-1)d]$ }

                                    ⇒  $2a + 12d = \frac{234*2}{13}$

                                    ⇒ 2*(3 - 12*d) +12*d = 36 {taking value of a from eq 1}

                                    ⇒ 6 - 24*d + 12*d = 36

                                    ⇒ 6 - 12*d = 36

                                     ⇒ d = $\frac{30}{-12}$ = -2.5

Now, putting value of d in equation 1 we get;

             ⇒ a = 3 - 12*(-2.5) = 3 + 30 = 33

Therefore, first term, a = 33 and common difference = -2.5 .

Also, sum of first 21 terms, $S_2_1$ = $\frac{21}{2} [2*33 + (21-1)*(-2.5)]$        

                                                  = $\frac{21}{2} [66 - 50]$ = 168 .

Therefore, sum of first 21 terms = 168.                                        

                 

Answer 2

Answer:

Common Difference is 2.5

Sum of first 21 terms is 168

Step-by-step explanation:

God Dammit just read the previous answer to this question .Jeez why do people even scroll after reading the correct answer