Question

The first and last terms of an arithmetic progression are -23 and 42. What is the sum of the series if it has 14 terms ?

Answer 1

Answer:

sum of the given A.P series Sn=133

Step-by-step explanation:

Answer 2

The sum of the first fourteen terms of AP is 133.

Given:

• The first and last terms of an arithmetic progression are -23 and 42.

To find:

• What is the sum of the series if it has 14 terms ?

Solution:

Concept/formula to be used:

Sum of first n terms of AP:

$\bf S_n=\frac{n}{2} (a + l)$

here,

a: first term

l: last term

Step 1:

Write the given terms.

ATQ

First term $\bf a = - 23$

Last term $\bf l = 42$

Number of terms $\bf n = 14$

Step 2:

Find the sum of AP upto 14 terms.

Put the values in the formula.

$S_{14} = \frac{14}{2} ( - 23 + 42)$

$S_{14} = 7 \times 19$

$\bf S_{14} = 133$

Thus,

Sum of first fourteen terms of AP is 133.

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