Question

find the 50 th term and the sum of first 50 term of AP. AP. 11,16, 21,26.​

Answer 1

Given ,

• First term (a) = 11
• Common difference (d) = 5

We know that , the first n terms of an AP is given by

$\large \mathtt{ \fbox{ a_{n} = a + (n - 1)d}}$

Thus ,

$\sf \mapsto a_{50} = 11 + (50 - 1)5 \\ \\\sf \mapsto a_{50} =11 + (49) \times 5 \\ \\\sf \mapsto a_{50} =11 + 245 \\ \\ \sf \mapsto a_{50} = 256$

Hence , the 50th term of an AP is 256

The sum of first n term of an AP is given by

$\large \mathtt{ \fbox{ S_{n} = \frac{n}{2} (a + l)}}$

Thus ,

➡S = 50/2 × (11 + 256)

➡S = 25 × 267

➡S = 6675

Hence , the sum of first 50 terms of an AP is 6675