Question

Find the 11th term from the end in the AP 56,63,70,...,329.

Answer 1

Hint: To find 11th term from the end we will approach same as we are doing from first term only we have to take last term as the first term and the common difference is previous term minus the next term and take n equal to 11 and calculate the value of 11th term by using the nth term formula in AP.

Complete step-by-step answer:
The given AP is 56, 63, 70,……….329.
Here we have to find the 11th term from the end
So suppose that first term (a) =329
The common difference (d)=56-63=63-70=-7
Number of terms (n)=11
Now we know that the nth term of an AP is
Nth term= \[{t_n} = a + \left( {n - 1} \right)d\]
On putting the given value we get
$
\Rightarrow {t_{11}} = 329 + \left( {11 - 1} \right)\left( { - 7} \right) \\
\Rightarrow {t_{11}} = 329 - 10 \times 7 \\
$
On simplifying the we get,
$
\Rightarrow {t_{11}} = 329 - 70 \\
\Rightarrow {t_{11}} = 259 \\
$
So the 11th term from the end is 259

Note: The 11th term from the end also can be calculated by the first term as 56 only we have to do that we have to find the 11th term from the end that we can calculate by calculating the total number of terms present in the AP then we move to 11th term from the end and find the position of that term from the beginning and use the same formula to calculate the 11th term from the end.