Question

An ap consists of 21 terms the sum of the three terms in the middle is 129 and the last 3 years to 37 find the ap

Answer 1

Answer:AP: 3, 7, 10.... 83

Step-by-step explanation:

In an AP, nth term is given by An=a+(n-1)d

Where a is first term and d is common difference.

n=21

Sum of last term is given by A19,A20,A21

A19+A20+A21=237

a+18d+a+19d+a+20d=237

3a+57d=237

a+19d=79 ...... eq(i)

Now sum of terms in middle is given by A10, A11, A12

A10+A11+A12= 129

a+9d+a+10d+a+11d= 129

3a+30=129

a+10d=43 ..... eq(ii)

Subtracting eq(ii) from eq(i)

a+19d= 79

a+10d= 43

-   -       -

_________

      9d=36

        d= 4

a+10*4=43

a=43-40

a=3

AP:3, 7, 10...... 83

Hope this helps!!